Title:
Algebra 1 : groups, rings, fields and arithmetic / Ramji Lal. Algebra One
Algebra One Algebra One
Infosys Science Foundation Series Algebra One
Infosys Science Foundation Series in Mathematical Sciences Algebra One
Infosys Science Foundation Series. Algebra One
Author:
Lal, Ramji, author.
General Notes:
Includes bibliographical references and index.
Chapter 1. Language of mathematics 1 (Logic) -- Chapter 2. Language Of Mathematics 2 (Set Theory) -- Chapter 3. Number System -- Chapter 4. Group Theory -- Chapter 5. Fundamental Theorems -- Chapter 6. Permutation groups and Classical Groups -- Chapter 7. Elementary Theory of Rings and Fields -- Chapter 8. Number Theory 2 -- Chapter 9. Structure theory of groups -- Chapter 10. Structure theory continued -- Chapter 11. Arithmetic in Rings.
This is the first in a series of three volumes dealing with important topics in algebra. It offers an introduction to the foundations of mathematics together with the fundamental algebraic structures, namely groups, rings, fields, and arithmetic. Intended as a text for undergraduate and graduate students of mathematics, it discusses all major topics in algebra with numerous motivating illustrations and exercises to enable readers to acquire a good understanding of the basic algebraic structures, which they can then use to find the exact or the most realistic solutions to their problems.
Publisher:
Springer,
Publication Place:
Singapore :
ISBN:
9789811042522
9811042527
ISSN:
23636149
Subject:
Group theory.
Rings (Algebra)
Algebraic fields.
Algebraic fields.
Group theory.
Rings (Algebra)
Series:
Infosys Science Foundation Series
Infosys Science Foundation Series in Mathematical Sciences
Infosys Science Foundation Series.
Contents:
Chapter 1. Language of mathematics 1 (Logic) -- Chapter 2. Language Of Mathematics 2 (Set Theory) -- Chapter 3. Number System -- Chapter 4. Group Theory -- Chapter 5. Fundamental Theorems -- Chapter 6. Permutation groups and Classical Groups -- Chapter 7. Elementary Theory of Rings and Fields -- Chapter 8. Number Theory 2 -- Chapter 9. Structure theory of groups -- Chapter 10. Structure theory continued -- Chapter 11. Arithmetic in Rings.
Physical Description:
xvii, 433 pages : illustrations ;
Publication Date:
[2017]
�2017
Title:
Algebra 2 : linear algebra, Galois theory, representation theory, group extensions and schur multiplier / Ramji Lal.
Infosys Science Foundation series
Infosys Science Foundation Series in Mathematical Sciences
Infosys Science Foundation series. Mathematical Sciences.
Author:
Lal, Ramji, author.
General Notes:
Includes bibliographical references and index.
Chapter 1. Vector Space -- Chapter 2. Matrices and Linear Equations -- Chapter 3. Linear Transformations -- Chapter 4. Inner Product Space -- Chapter 5. Determinants and Forms -- Chapter 6. Canonical Forms, Jordan and Rational Forms -- Chapter 7. General Linear Algebra -- Chapter 8. Field Theory, Galois Theory -- Chapter 9. Representation Theory of Finite Groups -- Chapter 10. Group Extensions and Schur Multiplier.
This is the second in a series of three volumes dealing with important topics in algebra. Volume 2 is an introduction to linear algebra (including linear algebra over rings), Galois theory, representation theory, and the theory of group extensions. The section on linear algebra (chapters 1-5) does not require any background material from Algebra 1, except an understanding of set theory. Linear algebra is the most applicable branch of mathematics, and it is essential for students of science and engineering As such, the text can be used for one-semester courses for these students. The remaining part of the volume discusses Jordan and rational forms, general linear algebra (linear algebra over rings), Galois theory, representation theory (linear algebra over group algebras), and the theory of extension of groups follow linear algebra, and is suitable as a text for the second and third year students specializing in mathematics. .
Publisher:
Springer,
Publication Place:
Singapore :
ISBN:
9789811042553
9811042551
Subject:
Algebra.
Group theory.
Algebras, Linear.
Algebra.
Algebras, Linear.
Group theory.
Series:
Infosys Science Foundation series
Infosys Science Foundation Series in Mathematical Sciences
Infosys Science Foundation series. Mathematical Sciences.
Contents:
Chapter 1. Vector Space -- Chapter 2. Matrices and Linear Equations -- Chapter 3. Linear Transformations -- Chapter 4. Inner Product Space -- Chapter 5. Determinants and Forms -- Chapter 6. Canonical Forms, Jordan and Rational Forms -- Chapter 7. General Linear Algebra -- Chapter 8. Field Theory, Galois Theory -- Chapter 9. Representation Theory of Finite Groups -- Chapter 10. Group Extensions and Schur Multiplier.
Physical Description:
xviii, 432 pages : illustrations ;
Publication Date:
[2017]
�2017
Title:
Algebra 3 : homological algebra and its applications / Ramji Lal.
Infosys Science Foundation series
Infosys Science Foundation Series.
Author:
Lal, Ramji, author.
General Notes:
Includes bibliographical references and index.
Intro -- Preface -- Contents -- About the Author -- Notations -- 1 Homological Algebra 1 -- 1.1 Categories and Functors -- 1.2 Abelian Categories -- 1.3 Category of Chain Complexes and Homology -- 1.4 Extensions and the Functor EXT -- 2 Homological Algebra 2, Derived Functors -- 2.1 Resolutions and Extensions -- 2.2 Tensor and Tor Functors -- 2.3 Abstract Theory of Derived Functors -- 2.4 Kunneth Formula -- 2.5 Spectral Sequences -- 3 Homological Algebra 3: Examples and Applications -- 3.1 Polyhedrons and Simplicial Homology -- 3.2 Applications -- 3.3 Co-homology of Groups
3.4 Calculus and Co-homology -- 4 Sheaf Co-homology and Its Applications -- 4.1 Presheaves and Sheaves -- 4.2 Sheaf Co-homology and ech Co-homology -- 4.3 Algebraic Varieties -- 4.4 Schemes -- 4.5 Weil Conjectures and l-adic Co-homology -- Appendix Bibliography -- Index
This book, the third book in the four-volume series in algebra, deals with important topics in homological algebra, including abstract theory of derived functors, sheaf co-homology, and an introduction to etale and l-adic co-homology. It contains four chapters which discuss homology theory in an abelian category together with some important and fundamental applications in geometry, topology, algebraic geometry (including basics in abstract algebraic geometry), and group theory. The book will be of value to graduate and higher undergraduate students specializing in any branch of mathematics. The author has tried to make the book self-contained by introducing relevant concepts and results required. Prerequisite knowledge of the basics of algebra, linear algebra, topology, and calculus of several variables will be useful.
Online resource; title from PDF title page (SpringerLink, viewed March 25, 2021).
Publisher:
Springer,
Publication Place:
Singapore :
ISBN:
9789813363267
9813363266
9789813363274
9813363274
9789813363281
9813363282
9813363258
9789813363250
Subject:
Algebra, Homological.
Algebra, Homological.
�Algebra homol�ogica.
Series:
Infosys Science Foundation series
Infosys Science Foundation Series.
Contents:
Intro -- Preface -- Contents -- About the Author -- Notations -- 1 Homological Algebra 1 -- 1.1 Categories and Functors -- 1.2 Abelian Categories -- 1.3 Category of Chain Complexes and Homology -- 1.4 Extensions and the Functor EXT -- 2 Homological Algebra 2, Derived Functors -- 2.1 Resolutions and Extensions -- 2.2 Tensor and Tor Functors -- 2.3 Abstract Theory of Derived Functors -- 2.4 Kunneth Formula -- 2.5 Spectral Sequences -- 3 Homological Algebra 3: Examples and Applications -- 3.1 Polyhedrons and Simplicial Homology -- 3.2 Applications -- 3.3 Co-homology of Groups
3.4 Calculus and Co-homology -- 4 Sheaf Co-homology and Its Applications -- 4.1 Presheaves and Sheaves -- 4.2 Sheaf Co-homology and ech Co-homology -- 4.3 Algebraic Varieties -- 4.4 Schemes -- 4.5 Weil Conjectures and l-adic Co-homology -- Appendix Bibliography -- Index
Electronic Location:
https://doi.org/10.1007/978-981-33-6326-7
http://public.eblib.com/choice/PublicFullRecord.aspx?p=6510185
http://link.springer.com/10.1007/978-981-33-6326-7
https://link.springer.com/10.1007/978-981-33-6326-7
https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=2802602
Publication Date:
[2021]
There are no items available
Title:
Algebra, a graduate course / I. Martin Isaacs.
Author:
Isaacs, I. Martin, 1940-
General Notes:
Includes index., Includes index.
Publisher:
Brooks/Cole Pub. Co.,
Publication Place:
Pacific Grove, Calif. :
ISBN:
0534190022
Subject:
Algebra.
Contents:
Definitions and examples of groups -- Subgroups and cosets -- Homomorphisms -- Group actions -- The sylow theorems and p-groups -- Permutation groups -- New groups from old -- Solvable and nilpotent groups -- Transfer -- Operator groups and unique decompositions -- Module theory without rings -- Rigns, ideals, and modules -- Simple modules and primitive rings -- Artinian rings and projective modules -- An introduction to character theory -- Polynomial rings, PIDs, and UFDs -- Field extensions -- Galois theory -- Separability and inseparability --
Cyclotomy and geometric constructions -- Finite fields -- Roots, radicals, and real numbers -- Norms, traces, and discriminants -- Transcendental extensions -- The Artin-Schreier theorem -- Ideal theory -- Noetherian rings -- Integrality -- Dedekind domains -- Algebraic sets and the Nullstellensatz.
Physical Description:
xii, 516 p. : ill. ;
Publication Date:
c1994.
Title:
Algebra A Teaching and Source Book / by Ernest Shult, David Surowski.
Author:
Shult, Ernest. author.
Surowski, David. author.
SpringerLink (Online service)
General Notes:
Basics -- Basic Combinatorial Principles of Algebra -- Review of Elementary Group Properties -- Permutation Groups and Group Actions -- Normal Structure of Groups -- Generation in Groups -- Elementary Properties of Rings -- Elementary properties of Modules -- The Arithmetic of Integral Domains -- Principal Ideal Domains and Their Modules -- Theory of Fields -- Semiprime Rings -- Tensor Products.
This book presents a graduate-level course on modern algebra. It can be used as a teaching book – owing to the copious exercises – and as a source book for those who wish to use the major theorems of algebra. The course begins with the basic combinatorial principles of algebra: posets, chain conditions, Galois connections, and dependence theories. Here, the general Jordan–Holder Theorem becomes a theorem on interval measures of certain lower semilattices. This is followed by basic courses on groups, rings and modules; the arithmetic of integral domains; fields; the categorical point of view; and tensor products. Beginning with introductory concepts and examples, each chapter proceeds gradually towards its more complex theorems. Proofs progress step-by-step from first principles. Many interesting results reside in the exercises, for example, the proof that ideals in a Dedekind domain are generated by at most two elements. The emphasis throughout is on real understanding as opposed to memorizing a catechism and so some chapters offer curiosity-driven appendices for the self-motivated student.
Publisher:
Springer International Publishing : Imprint: Springer,
Publication Place:
Cham :
ISBN:
9783319197340
Subject:
Mathematics.
Algebra.
Associative rings.
Rings (Algebra).
Field theory (Physics).
Group theory.
Mathematics.
Associative Rings and Algebras.
Group Theory and Generalizations.
Field Theory and Polynomials.
Algebra.
Contents:
Basics -- Basic Combinatorial Principles of Algebra -- Review of Elementary Group Properties -- Permutation Groups and Group Actions -- Normal Structure of Groups -- Generation in Groups -- Elementary Properties of Rings -- Elementary properties of Modules -- The Arithmetic of Integral Domains -- Principal Ideal Domains and Their Modules -- Theory of Fields -- Semiprime Rings -- Tensor Products.
Physical Description:
XXII, 539 p. 6 illus. online resource.
Electronic Location:
http://dx.doi.org/10.1007/978-3-319-19734-0
Publication Date:
2015.
Title:
The Local Structure of Algebraic K-Theory by Bjørn Ian Dundas, Thomas G. Goodwillie, Randy McCarthy.
Algebra and Applications,
Algebra and Applications,
Author:
Dundas, Bjørn Ian. author.
Goodwillie, Thomas G. author.
McCarthy, Randy. author.
SpringerLink (Online service)
General Notes:
Algebraic K-theory -- Gamma-spaces and S-algebras -- Reductions -- Topological Hochschild Homology -- The Trace K → THH -- Topological Cyclic Homology -- The Comparison of K-theory and TC.
Algebraic K-theory encodes important invariants for several mathematical disciplines, spanning from geometric topology and functional analysis to number theory and algebraic geometry. As is commonly encountered, this powerful mathematical object is very hard to calculate. Apart from Quillen's calculations of finite fields and Suslin's calculation of algebraically closed fields, few complete calculations were available before the discovery of homological invariants offered by motivic cohomology and topological cyclic homology. This book covers the connection between algebraic K-theory and Bökstedt, Hsiang and Madsen's topological cyclic homology and proves that the difference between the theories are ‘locally constant’. The usefulness of this theorem stems from being more accessible for calculations than K-theory, and hence a single calculation of K-theory can be used with homological calculations to obtain a host of ‘nearby’ calculations in K-theory. For instance, Quillen's calculation of the K-theory of finite fields gives rise to Hesselholt and Madsen's calculations for local fields, and Voevodsky's calculations for the integers give insight into the diffeomorphisms of manifolds. In addition to the proof of the full integral version of the local correspondence between K-theory and topological cyclic homology, the book provides an introduction to the necessary background in algebraic K-theory and highly structured homotopy theory; collecting all necessary tools into one common framework. It relies on simplicial techniques, and contains an appendix summarizing the methods widely used in the field. The book is intended for graduate students and scientists interested in algebraic K-theory, and presupposes a basic knowledge of algebraic topology.
Publisher:
Springer London : Imprint: Springer,
Publication Place:
London :
ISBN:
9781447143932
Subject:
Mathematics.
Algebra.
K-theory.
Algebraic topology.
Mathematics.
K-Theory.
Algebraic topology.
Category Theory, Homological Algebra.
Series:
Algebra and Applications, 18
Algebra and Applications, 18
Contents:
Algebraic K-theory -- Gamma-spaces and S-algebras -- Reductions -- Topological Hochschild Homology -- The Trace K → THH -- Topological Cyclic Homology -- The Comparison of K-theory and TC.
Physical Description:
XV, 435 p. 5 illus. online resource.
Electronic Location:
http://dx.doi.org/10.1007/978-1-4471-4393-2
Publication Date:
2012.
Title:
The Local Structure of Algebraic K-Theory by Bjørn Ian Dundas, Thomas G. Goodwillie, Randy McCarthy.
Algebra and Applications,
Algebra and Applications,
Author:
Dundas, Bjørn Ian. author.
Goodwillie, Thomas G. author.
McCarthy, Randy. author.
SpringerLink (Online service)
General Notes:
Algebraic K-theory -- Gamma-spaces and S-algebras -- Reductions -- Topological Hochschild Homology -- The Trace K → THH -- Topological Cyclic Homology -- The Comparison of K-theory and TC.
Algebraic K-theory encodes important invariants for several mathematical disciplines, spanning from geometric topology and functional analysis to number theory and algebraic geometry. As is commonly encountered, this powerful mathematical object is very hard to calculate. Apart from Quillen's calculations of finite fields and Suslin's calculation of algebraically closed fields, few complete calculations were available before the discovery of homological invariants offered by motivic cohomology and topological cyclic homology. This book covers the connection between algebraic K-theory and Bökstedt, Hsiang and Madsen's topological cyclic homology and proves that the difference between the theories are ‘locally constant’. The usefulness of this theorem stems from being more accessible for calculations than K-theory, and hence a single calculation of K-theory can be used with homological calculations to obtain a host of ‘nearby’ calculations in K-theory. For instance, Quillen's calculation of the K-theory of finite fields gives rise to Hesselholt and Madsen's calculations for local fields, and Voevodsky's calculations for the integers give insight into the diffeomorphisms of manifolds. In addition to the proof of the full integral version of the local correspondence between K-theory and topological cyclic homology, the book provides an introduction to the necessary background in algebraic K-theory and highly structured homotopy theory; collecting all necessary tools into one common framework. It relies on simplicial techniques, and contains an appendix summarizing the methods widely used in the field. The book is intended for graduate students and scientists interested in algebraic K-theory, and presupposes a basic knowledge of algebraic topology.
Publisher:
Springer London : Imprint: Springer,
Publication Place:
London :
ISBN:
9781447143932
Subject:
Mathematics.
Algebra.
K-theory.
Algebraic topology.
Mathematics.
K-Theory.
Algebraic topology.
Category Theory, Homological Algebra.
Series:
Algebra and Applications, 18
Algebra and Applications, 18
Contents:
Algebraic K-theory -- Gamma-spaces and S-algebras -- Reductions -- Topological Hochschild Homology -- The Trace K → THH -- Topological Cyclic Homology -- The Comparison of K-theory and TC.
Physical Description:
XV, 435 p. 5 illus. online resource.
Electronic Location:
http://dx.doi.org/10.1007/978-1-4471-4393-2
Publication Date:
2012.
Title:
Syzygies and Homotopy Theory by F.E.A. Johnson.
Algebra and Applications,
Algebra and Applications,
Author:
Johnson, F.E.A. author.
SpringerLink (Online service)
General Notes:
Preliminaries -- The restricted linear group -- The calculus of corners and squares -- Extensions of modules -- The derived module category -- Finiteness conditions -- The Swan mapping -- Classification of algebraic complexes -- Rings with stably free cancellation -- Group rings of cyclic groups -- Group rings of dihedral groups -- Group rings of quaternionic groups -- Parametrizing W1 (Z) : generic case -- Parametrizing W1 (Z) : singular case -- Generalized Swan modules -- Parametrizing W1 (Z) : G = C¥ ´ F -- Conclusion .
The most important invariant of a topological space is its fundamental group. When this is trivial, the resulting homotopy theory is well researched and familiar. In the general case, however, homotopy theory over nontrivial fundamental groups is much more problematic and far less well understood. Syzygies and Homotopy Theory explores the problem of nonsimply connected homotopy in the first nontrivial cases and presents, for the first time, a systematic rehabilitation of Hilbert's method of syzygies in the context of non-simply connected homotopy theory. The first part of the book is theoretical, formulated to allow a general finitely presented group as a fundamental group. The innovation here is to regard syzygies as stable modules rather than minimal modules. Inevitably this forces a reconsideration of the problems of noncancellation; these are confronted in the second, practical, part of the book. In particular, the second part of the book considers how the theory works out in detail for the specific examples Fn ´F where Fn is a free group of rank n and F is finite. Another innovation is to parametrize the first syzygy in terms of the more familiar class of stably free modules. Furthermore, detailed description of these stably free modules is effected by a suitable modification of the method of Milnor squares. The theory developed within this book has potential applications in various branches of algebra, including homological algebra, ring theory and K-theory. Syzygies and Homotopy Theory will be of interest to researchers and also to graduate students with a background in algebra and algebraic topology.
Publisher:
Springer London,
Publication Place:
London :
ISBN:
9781447122944
Subject:
Mathematics.
Algebra.
Group theory.
Mathematics.
Group Theory and Generalizations.
Commutative Rings and Algebras.
Series:
Algebra and Applications, 17
Algebra and Applications, 17
Contents:
Preliminaries -- The restricted linear group -- The calculus of corners and squares -- Extensions of modules -- The derived module category -- Finiteness conditions -- The Swan mapping -- Classification of algebraic complexes -- Rings with stably free cancellation -- Group rings of cyclic groups -- Group rings of dihedral groups -- Group rings of quaternionic groups -- Parametrizing W1 (Z) : generic case -- Parametrizing W1 (Z) : singular case -- Generalized Swan modules -- Parametrizing W1 (Z) : G = C¥ ´ F -- Conclusion .
Physical Description:
XXIV, 296 p. online resource.
Electronic Location:
http://dx.doi.org/10.1007/978-1-4471-2294-4
Publication Date:
2012.
Title:
Syzygies and Homotopy Theory by F.E.A. Johnson.
Algebra and Applications,
Algebra and Applications,
Author:
Johnson, F.E.A. author.
SpringerLink (Online service)
General Notes:
Preliminaries -- The restricted linear group -- The calculus of corners and squares -- Extensions of modules -- The derived module category -- Finiteness conditions -- The Swan mapping -- Classification of algebraic complexes -- Rings with stably free cancellation -- Group rings of cyclic groups -- Group rings of dihedral groups -- Group rings of quaternionic groups -- Parametrizing W1 (Z) : generic case -- Parametrizing W1 (Z) : singular case -- Generalized Swan modules -- Parametrizing W1 (Z) : G = C¥ ´ F -- Conclusion .
The most important invariant of a topological space is its fundamental group. When this is trivial, the resulting homotopy theory is well researched and familiar. In the general case, however, homotopy theory over nontrivial fundamental groups is much more problematic and far less well understood. Syzygies and Homotopy Theory explores the problem of nonsimply connected homotopy in the first nontrivial cases and presents, for the first time, a systematic rehabilitation of Hilbert's method of syzygies in the context of non-simply connected homotopy theory. The first part of the book is theoretical, formulated to allow a general finitely presented group as a fundamental group. The innovation here is to regard syzygies as stable modules rather than minimal modules. Inevitably this forces a reconsideration of the problems of noncancellation; these are confronted in the second, practical, part of the book. In particular, the second part of the book considers how the theory works out in detail for the specific examples Fn ´F where Fn is a free group of rank n and F is finite. Another innovation is to parametrize the first syzygy in terms of the more familiar class of stably free modules. Furthermore, detailed description of these stably free modules is effected by a suitable modification of the method of Milnor squares. The theory developed within this book has potential applications in various branches of algebra, including homological algebra, ring theory and K-theory. Syzygies and Homotopy Theory will be of interest to researchers and also to graduate students with a background in algebra and algebraic topology.
Publisher:
Springer London,
Publication Place:
London :
ISBN:
9781447122944
Subject:
Mathematics.
Algebra.
Group theory.
Mathematics.
Group Theory and Generalizations.
Commutative Rings and Algebras.
Series:
Algebra and Applications, 17
Algebra and Applications, 17
Contents:
Preliminaries -- The restricted linear group -- The calculus of corners and squares -- Extensions of modules -- The derived module category -- Finiteness conditions -- The Swan mapping -- Classification of algebraic complexes -- Rings with stably free cancellation -- Group rings of cyclic groups -- Group rings of dihedral groups -- Group rings of quaternionic groups -- Parametrizing W1 (Z) : generic case -- Parametrizing W1 (Z) : singular case -- Generalized Swan modules -- Parametrizing W1 (Z) : G = C¥ ´ F -- Conclusion .
Physical Description:
XXIV, 296 p. online resource.
Electronic Location:
http://dx.doi.org/10.1007/978-1-4471-2294-4
Publication Date:
2012.
Title:
Representation Theory A Homological Algebra Point of View / by Alexander Zimmermann.
Algebra and Applications,
Algebra and Applications,
Author:
Zimmermann, Alexander. author.
SpringerLink (Online service)
General Notes:
Rings, Algebras and Modules -- Modular Representations of Finite Groups -- Abelian and Triangulated Categories -- Morita theory -- Stable Module Categories -- Derived Equivalences.
 Introducing the representation theory of groups and finite dimensional algebras, this book first studies basic non-commutative ring theory, covering the necessary background of elementary homological algebra and representations of groups to block theory. It further discusses vertices, defect groups, Green and Brauer correspondences and Clifford theory. Whenever possible the statements are presented in a general setting for more general algebras, such as symmetric finite dimensional algebras over a field. Then, abelian and derived categories are introduced in detail and are used to explain stable module categories, as well as derived categories and their main invariants and links between them. Group theoretical applications of these theories are given – such as the structure of blocks of cyclic defect groups – whenever appropriate. Overall, many methods from the representation theory of algebras are introduced. Representation Theory assumes only the most basic knowledge of linear algebra, groups, rings and fields, and guides the reader in the use of categorical equivalences in the representation theory of groups and algebras. As the book is based on lectures, it will be accessible to any graduate student in algebra and can be used for self-study as well as for classroom use.
Publisher:
Springer International Publishing : Imprint: Springer,
Publication Place:
Cham :
ISBN:
9783319079684
Subject:
Mathematics.
Algebra.
Associative rings.
Rings (Algebra).
Category theory (Mathematics).
Homological algebra.
Group theory.
Mathematics.
Algebra.
Associative Rings and Algebras.
Category Theory, Homological Algebra.
Group Theory and Generalizations.
Series:
Algebra and Applications, 19
Algebra and Applications, 19
Contents:
Rings, Algebras and Modules -- Modular Representations of Finite Groups -- Abelian and Triangulated Categories -- Morita theory -- Stable Module Categories -- Derived Equivalences.
Physical Description:
XX, 707 p. 59 illus. online resource.
Electronic Location:
http://dx.doi.org/10.1007/978-3-319-07968-4
Publication Date:
2014.
Title:
Representation Theory A Homological Algebra Point of View / by Alexander Zimmermann.
Algebra and Applications,
Algebra and Applications,
Author:
Zimmermann, Alexander. author.
SpringerLink (Online service)
General Notes:
Rings, Algebras and Modules -- Modular Representations of Finite Groups -- Abelian and Triangulated Categories -- Morita theory -- Stable Module Categories -- Derived Equivalences.
 Introducing the representation theory of groups and finite dimensional algebras, this book first studies basic non-commutative ring theory, covering the necessary background of elementary homological algebra and representations of groups to block theory. It further discusses vertices, defect groups, Green and Brauer correspondences and Clifford theory. Whenever possible the statements are presented in a general setting for more general algebras, such as symmetric finite dimensional algebras over a field. Then, abelian and derived categories are introduced in detail and are used to explain stable module categories, as well as derived categories and their main invariants and links between them. Group theoretical applications of these theories are given – such as the structure of blocks of cyclic defect groups – whenever appropriate. Overall, many methods from the representation theory of algebras are introduced. Representation Theory assumes only the most basic knowledge of linear algebra, groups, rings and fields, and guides the reader in the use of categorical equivalences in the representation theory of groups and algebras. As the book is based on lectures, it will be accessible to any graduate student in algebra and can be used for self-study as well as for classroom use.
Publisher:
Springer International Publishing : Imprint: Springer,
Publication Place:
Cham :
ISBN:
9783319079684
Subject:
Mathematics.
Algebra.
Associative rings.
Rings (Algebra).
Category theory (Mathematics).
Homological algebra.
Group theory.
Mathematics.
Algebra.
Associative Rings and Algebras.
Category Theory, Homological Algebra.
Group Theory and Generalizations.
Series:
Algebra and Applications, 19
Algebra and Applications, 19
Contents:
Rings, Algebras and Modules -- Modular Representations of Finite Groups -- Abelian and Triangulated Categories -- Morita theory -- Stable Module Categories -- Derived Equivalences.
Physical Description:
XX, 707 p. 59 illus. online resource.
Electronic Location:
http://dx.doi.org/10.1007/978-3-319-07968-4
Publication Date:
2014.
Title:
Rigid Cohomology over Laurent Series Fields by Christopher Lazda, Ambrus Pál.
Algebra and Applications,
Algebra and Applications,
Author:
Lazda, Christopher. author.
Pál, Ambrus. author.
SpringerLink (Online service)
General Notes:
Introduction -- First definitions and basic properties -- Finiteness with coefficients via a local monodromy theorem -- The overconvergent site, descent, and cohomology with compact support -- Absolute coefficients and arithmetic applications -- Rigid cohomology -- Adic spaces and rigid spaces -- Cohomological descent -- Index.
In this monograph, the authors develop a new theory of p-adic cohomology for varieties over Laurent series fields in positive characteristic, based on Berthelot's theory of rigid cohomology. Many major fundamental properties of these cohomology groups are proven, such as finite dimensionality and cohomological descent, as well as interpretations in terms of Monsky-Washnitzer cohomology and Le Stum's overconvergent site. Applications of this new theory to arithmetic questions, such as l-independence and the weight monodromy conjecture, are also discussed. The construction of these cohomology groups, analogous to the Galois representations associated to varieties over local fields in mixed characteristic, fills a major gap in the study of arithmetic cohomology theories over function fields. By extending the scope of existing methods, the results presented here also serve as a first step towards a more general theory of p-adic cohomology over non-perfect ground fields. Rigid Cohomology over Laurent Series Fields will provide a useful tool for anyone interested in the arithmetic of varieties over local fields of positive characteristic. Appendices on important background material such as rigid cohomology and adic spaces make it as self-contained as possible, and an ideal starting point for graduate students looking to explore aspects of the classical theory of rigid cohomology and with an eye towards future research in the subject.
Publisher:
Springer International Publishing : Imprint: Springer,
Publication Place:
Cham :
ISBN:
9783319309514
Subject:
Mathematics.
Algebraic geometry.
Number theory.
Mathematics.
Algebraic Geometry.
Number theory.
Series:
Algebra and Applications, 21
Algebra and Applications, 21
Contents:
Introduction -- First definitions and basic properties -- Finiteness with coefficients via a local monodromy theorem -- The overconvergent site, descent, and cohomology with compact support -- Absolute coefficients and arithmetic applications -- Rigid cohomology -- Adic spaces and rigid spaces -- Cohomological descent -- Index.
Physical Description:
X, 267 p. online resource.
Electronic Location:
http://dx.doi.org/10.1007/978-3-319-30951-4
Publication Date:
2016.
Title:
Rigid Cohomology over Laurent Series Fields by Christopher Lazda, Ambrus Pál.
Algebra and Applications,
Algebra and Applications,
Author:
Lazda, Christopher. author.
Pál, Ambrus. author.
SpringerLink (Online service)
General Notes:
Introduction -- First definitions and basic properties -- Finiteness with coefficients via a local monodromy theorem -- The overconvergent site, descent, and cohomology with compact support -- Absolute coefficients and arithmetic applications -- Rigid cohomology -- Adic spaces and rigid spaces -- Cohomological descent -- Index.
In this monograph, the authors develop a new theory of p-adic cohomology for varieties over Laurent series fields in positive characteristic, based on Berthelot's theory of rigid cohomology. Many major fundamental properties of these cohomology groups are proven, such as finite dimensionality and cohomological descent, as well as interpretations in terms of Monsky-Washnitzer cohomology and Le Stum's overconvergent site. Applications of this new theory to arithmetic questions, such as l-independence and the weight monodromy conjecture, are also discussed. The construction of these cohomology groups, analogous to the Galois representations associated to varieties over local fields in mixed characteristic, fills a major gap in the study of arithmetic cohomology theories over function fields. By extending the scope of existing methods, the results presented here also serve as a first step towards a more general theory of p-adic cohomology over non-perfect ground fields. Rigid Cohomology over Laurent Series Fields will provide a useful tool for anyone interested in the arithmetic of varieties over local fields of positive characteristic. Appendices on important background material such as rigid cohomology and adic spaces make it as self-contained as possible, and an ideal starting point for graduate students looking to explore aspects of the classical theory of rigid cohomology and with an eye towards future research in the subject.
Publisher:
Springer International Publishing : Imprint: Springer,
Publication Place:
Cham :
ISBN:
9783319309514
Subject:
Mathematics.
Algebraic geometry.
Number theory.
Mathematics.
Algebraic Geometry.
Number theory.
Series:
Algebra and Applications, 21
Algebra and Applications, 21
Contents:
Introduction -- First definitions and basic properties -- Finiteness with coefficients via a local monodromy theorem -- The overconvergent site, descent, and cohomology with compact support -- Absolute coefficients and arithmetic applications -- Rigid cohomology -- Adic spaces and rigid spaces -- Cohomological descent -- Index.
Physical Description:
X, 267 p. online resource.
Electronic Location:
http://dx.doi.org/10.1007/978-3-319-30951-4
Publication Date:
2016.
Title:
Foundations of Commutative Rings and Their Modules by Fanggui Wang, Hwankoo Kim.
Algebra and Applications,
Algebra and Applications,
Author:
Wang, Fanggui. author.
Kim, Hwankoo. author.
SpringerLink (Online service)
General Notes:
1 Basic Theory of Rings and Modules -- 2 The Category of Modules -- 3 Homological Methods -- 4 Basic Theory of Noetherian Rings -- 5 Extensions of Rings -- 6 w-Modules over Commutative Rings -- 7 Multiplicative Ideal Theory over Integral Domains -- 8 Structural Theory of Milnor Squares -- 9 Coherent Rings with Finite Weak Global Dimension -- 10 The Grothendieck Group of a Ring -- 11 Relative Homological Algebra -- References -- Index of Symbols -- Index.
This book provides an introduction to the basics and recent developments of commutative algebra. A glance at the contents of the first five chapters shows that the topics covered are ones that usually are included in any commutative algebra text. However, the contents of this book differ significantly from most commutative algebra texts: namely, its treatment of the Dedekind–Mertens formula, the (small) finitistic dimension of a ring, Gorenstein rings, valuation overrings and the valuative dimension, and Nagata rings. Going further, Chapter 6 presents w-modules over commutative rings as they can be most commonly used by torsion theory and multiplicative ideal theory. Chapter 7 deals with multiplicative ideal theory over integral domains. Chapter 8 collects various results of the pullbacks, especially Milnor squares and D+M constructions, which are probably the most important example-generating machines. In Chapter 9, coherent rings with finite weak global dimensions are probed, and the local ring of weak global dimension two is elaborated on by combining homological tricks and methods of star operation theory. Chapter 10 is devoted to the Grothendieck group of a commutative ring. In particular, the Bass–Quillen problem is discussed. Finally, Chapter 11 aims to introduce relative homological algebra, especially where the related concepts of integral domains which appear in classical ideal theory are defined and investigated by using the class of Gorenstein projective modules. Each section of the book is followed by a selection of exercises of varying degrees of difficulty. This book will appeal to a wide readership from graduate students to academic researchers who are interested in studying commutative algebra.
Publisher:
Springer Singapore : Imprint: Springer,
Publication Place:
Singapore :
ISBN:
9789811033377
Subject:
Mathematics.
Category theory (Mathematics).
Homological algebra.
Commutative algebra.
Commutative rings.
Mathematics.
Commutative Rings and Algebras.
Category Theory, Homological Algebra.
Series:
Algebra and Applications, 22
Algebra and Applications, 22
Contents:
1 Basic Theory of Rings and Modules -- 2 The Category of Modules -- 3 Homological Methods -- 4 Basic Theory of Noetherian Rings -- 5 Extensions of Rings -- 6 w-Modules over Commutative Rings -- 7 Multiplicative Ideal Theory over Integral Domains -- 8 Structural Theory of Milnor Squares -- 9 Coherent Rings with Finite Weak Global Dimension -- 10 The Grothendieck Group of a Ring -- 11 Relative Homological Algebra -- References -- Index of Symbols -- Index.
Physical Description:
XXII, 699 p. 273 illus. online resource.
Electronic Location:
http://dx.doi.org/10.1007/978-981-10-3337-7
Publication Date:
2016.
Title:
Foundations of Commutative Rings and Their Modules by Fanggui Wang, Hwankoo Kim.
Algebra and Applications,
Algebra and Applications,
Author:
Wang, Fanggui. author.
Kim, Hwankoo. author.
SpringerLink (Online service)
General Notes:
1 Basic Theory of Rings and Modules -- 2 The Category of Modules -- 3 Homological Methods -- 4 Basic Theory of Noetherian Rings -- 5 Extensions of Rings -- 6 w-Modules over Commutative Rings -- 7 Multiplicative Ideal Theory over Integral Domains -- 8 Structural Theory of Milnor Squares -- 9 Coherent Rings with Finite Weak Global Dimension -- 10 The Grothendieck Group of a Ring -- 11 Relative Homological Algebra -- References -- Index of Symbols -- Index.
This book provides an introduction to the basics and recent developments of commutative algebra. A glance at the contents of the first five chapters shows that the topics covered are ones that usually are included in any commutative algebra text. However, the contents of this book differ significantly from most commutative algebra texts: namely, its treatment of the Dedekind–Mertens formula, the (small) finitistic dimension of a ring, Gorenstein rings, valuation overrings and the valuative dimension, and Nagata rings. Going further, Chapter 6 presents w-modules over commutative rings as they can be most commonly used by torsion theory and multiplicative ideal theory. Chapter 7 deals with multiplicative ideal theory over integral domains. Chapter 8 collects various results of the pullbacks, especially Milnor squares and D+M constructions, which are probably the most important example-generating machines. In Chapter 9, coherent rings with finite weak global dimensions are probed, and the local ring of weak global dimension two is elaborated on by combining homological tricks and methods of star operation theory. Chapter 10 is devoted to the Grothendieck group of a commutative ring. In particular, the Bass–Quillen problem is discussed. Finally, Chapter 11 aims to introduce relative homological algebra, especially where the related concepts of integral domains which appear in classical ideal theory are defined and investigated by using the class of Gorenstein projective modules. Each section of the book is followed by a selection of exercises of varying degrees of difficulty. This book will appeal to a wide readership from graduate students to academic researchers who are interested in studying commutative algebra.
Publisher:
Springer Singapore : Imprint: Springer,
Publication Place:
Singapore :
ISBN:
9789811033377
Subject:
Mathematics.
Category theory (Mathematics).
Homological algebra.
Commutative algebra.
Commutative rings.
Mathematics.
Commutative Rings and Algebras.
Category Theory, Homological Algebra.
Series:
Algebra and Applications, 22
Algebra and Applications, 22
Contents:
1 Basic Theory of Rings and Modules -- 2 The Category of Modules -- 3 Homological Methods -- 4 Basic Theory of Noetherian Rings -- 5 Extensions of Rings -- 6 w-Modules over Commutative Rings -- 7 Multiplicative Ideal Theory over Integral Domains -- 8 Structural Theory of Milnor Squares -- 9 Coherent Rings with Finite Weak Global Dimension -- 10 The Grothendieck Group of a Ring -- 11 Relative Homological Algebra -- References -- Index of Symbols -- Index.
Physical Description:
XXII, 699 p. 273 illus. online resource.
Electronic Location:
http://dx.doi.org/10.1007/978-981-10-3337-7
Publication Date:
2016.
Title:
Graded Syzygies by Irena Peeva.
Algebra and Applications ;
Algebra and Applications ;
Author:
Peeva, Irena.
SpringerLink (Online service)
General Notes:
<p>Graded Free Resolutions -- Hilbert Functions -- Monomial Resolutions -- Syzygies of Toric Ideals</p>.
<p>The study of free resolutions is a core and beautiful area in Commutative Algebra. The main goal of this book is to inspire the readers and develop their intuition about syzygies and Hilbert functions. Many examples are given in order to illustrate ideas and key concepts.</p><p>A valuable feature of the book is the inclusion of open problems and conjectures; these provide a glimpse of exciting, and often challenging, research directions in the field. Three types of problems are presented: Conjectures, Problems, and Open-Ended Problems. The latter do not describe specific problems but point to interesting directions for exploration.</p><p>The first part of the monograph contains basic background material on graded free resolutions. Further coverage of topics includes syzygies over a polynomial ring, resolutions over quotient rings, lex ideals and Hilbert functions, compression, resolutions of monomial ideals, and syzygies of toric ideals. With a clear and self-contained exposition this text is intended for advanced graduate students and postdoctorates; it will be also of interest to senior mathematicians.</p>
Publisher:
Springer London,
Publication Place:
London :
ISBN:
9780857291776
Subject:
Mathematics.
Algebra.
Mathematics.
Commutative Rings and Algebras.
Series:
Algebra and Applications ; 14
Algebra and Applications ; 14
Contents:
<p>Graded Free Resolutions -- Hilbert Functions -- Monomial Resolutions -- Syzygies of Toric Ideals</p>.
Physical Description:
XII, 304 p. digital.
Electronic Location:
http://dx.doi.org/10.1007/978-0-85729-177-6
Publication Date:
2011.
Title:
Graded Syzygies by Irena Peeva.
Algebra and Applications ;
Algebra and Applications ;
Author:
Peeva, Irena.
SpringerLink (Online service)
General Notes:
<p>Graded Free Resolutions -- Hilbert Functions -- Monomial Resolutions -- Syzygies of Toric Ideals</p>.
<p>The study of free resolutions is a core and beautiful area in Commutative Algebra. The main goal of this book is to inspire the readers and develop their intuition about syzygies and Hilbert functions. Many examples are given in order to illustrate ideas and key concepts.</p><p>A valuable feature of the book is the inclusion of open problems and conjectures; these provide a glimpse of exciting, and often challenging, research directions in the field. Three types of problems are presented: Conjectures, Problems, and Open-Ended Problems. The latter do not describe specific problems but point to interesting directions for exploration.</p><p>The first part of the monograph contains basic background material on graded free resolutions. Further coverage of topics includes syzygies over a polynomial ring, resolutions over quotient rings, lex ideals and Hilbert functions, compression, resolutions of monomial ideals, and syzygies of toric ideals. With a clear and self-contained exposition this text is intended for advanced graduate students and postdoctorates; it will be also of interest to senior mathematicians.</p>
Publisher:
Springer London,
Publication Place:
London :
ISBN:
9780857291776
Subject:
Mathematics.
Algebra.
Mathematics.
Commutative Rings and Algebras.
Series:
Algebra and Applications ; 14
Algebra and Applications ; 14
Contents:
<p>Graded Free Resolutions -- Hilbert Functions -- Monomial Resolutions -- Syzygies of Toric Ideals</p>.
Physical Description:
XII, 304 p. digital.
Electronic Location:
http://dx.doi.org/10.1007/978-0-85729-177-6
Publication Date:
2011.
Title:
Representations of Hecke Algebras at Roots of Unity by Meinolf Geck, Nicolas Jacon.
Algebra and Applications ;
Algebra and Applications ;
Author:
Geck, Meinolf.
Jacon, Nicolas.
SpringerLink (Online service)
General Notes:
<p>Generic Iwahori–Hecke algebras -- Kazhdan–Lusztig cells and cellular bases -- Specialisations and decomposition maps -- Hecke algebras and finite groups of Lie type -- Representation theory of Ariki–Koike algebras -- Canonical bases in affine type <i>A </i>and Ariki’s theorem -- Decomposition numbers for exceptional types.</p>.
<p>The modular representation theory of Iwahori-Hecke algebras and this theory's connection to groups of Lie type is an area of rapidly expanding interest; it is one that has also seen a number of breakthroughs in recent years. In classifying the irreducible representations of Iwahori-Hecke algebras at roots of unity, this book is a particularly valuable addition to current research in this field. Using the framework provided by the Kazhdan-Lusztig theory of cells, the authors develop an analogue of James' (1970) "characteristic-free'' approach to the representation theory of Iwahori-Hecke algebras in general.</p><p>Presenting a systematic and unified treatment of representations of Hecke algebras at roots of unity, this book is unique in its approach and includes new results that have not yet been published in book form. It also serves as background reading to further active areas of current research such as the theory of affine Hecke algebras and Cherednik algebras.</p><p>The main results of this book are obtained by an interaction of several branches of mathematics, namely the theory of Fock spaces for quantum affine Lie algebras and Ariki's theorem, the combinatorics of crystal bases, the theory of Kazhdan-Lusztig bases and cells, and computational methods.</p><p>This book will be of use to researchers and graduate students in representation theory as well as any researchers outside of the field with an interest in Hecke algebras.</p>
Publisher:
Springer London,
Publication Place:
London :
ISBN:
9780857297167
Subject:
Mathematics.
Algebra.
Group theory.
Mathematics.
Group Theory and Generalizations.
Associative Rings and Algebras.
Series:
Algebra and Applications ; 15
Algebra and Applications ; 15
Contents:
<p>Generic Iwahori–Hecke algebras -- Kazhdan–Lusztig cells and cellular bases -- Specialisations and decomposition maps -- Hecke algebras and finite groups of Lie type -- Representation theory of Ariki–Koike algebras -- Canonical bases in affine type <i>A </i>and Ariki’s theorem -- Decomposition numbers for exceptional types.</p>.
Physical Description:
XII, 401p. 6 illus. digital.
Electronic Location:
http://dx.doi.org/10.1007/978-0-85729-716-7
Publication Date:
2011.
Title:
Representations of Hecke Algebras at Roots of Unity by Meinolf Geck, Nicolas Jacon.
Algebra and Applications ;
Algebra and Applications ;
Author:
Geck, Meinolf.
Jacon, Nicolas.
SpringerLink (Online service)
General Notes:
<p>Generic Iwahori–Hecke algebras -- Kazhdan–Lusztig cells and cellular bases -- Specialisations and decomposition maps -- Hecke algebras and finite groups of Lie type -- Representation theory of Ariki–Koike algebras -- Canonical bases in affine type <i>A </i>and Ariki’s theorem -- Decomposition numbers for exceptional types.</p>.
<p>The modular representation theory of Iwahori-Hecke algebras and this theory's connection to groups of Lie type is an area of rapidly expanding interest; it is one that has also seen a number of breakthroughs in recent years. In classifying the irreducible representations of Iwahori-Hecke algebras at roots of unity, this book is a particularly valuable addition to current research in this field. Using the framework provided by the Kazhdan-Lusztig theory of cells, the authors develop an analogue of James' (1970) "characteristic-free'' approach to the representation theory of Iwahori-Hecke algebras in general.</p><p>Presenting a systematic and unified treatment of representations of Hecke algebras at roots of unity, this book is unique in its approach and includes new results that have not yet been published in book form. It also serves as background reading to further active areas of current research such as the theory of affine Hecke algebras and Cherednik algebras.</p><p>The main results of this book are obtained by an interaction of several branches of mathematics, namely the theory of Fock spaces for quantum affine Lie algebras and Ariki's theorem, the combinatorics of crystal bases, the theory of Kazhdan-Lusztig bases and cells, and computational methods.</p><p>This book will be of use to researchers and graduate students in representation theory as well as any researchers outside of the field with an interest in Hecke algebras.</p>
Publisher:
Springer London,
Publication Place:
London :
ISBN:
9780857297167
Subject:
Mathematics.
Algebra.
Group theory.
Mathematics.
Group Theory and Generalizations.
Associative Rings and Algebras.
Series:
Algebra and Applications ; 15
Algebra and Applications ; 15
Contents:
<p>Generic Iwahori–Hecke algebras -- Kazhdan–Lusztig cells and cellular bases -- Specialisations and decomposition maps -- Hecke algebras and finite groups of Lie type -- Representation theory of Ariki–Koike algebras -- Canonical bases in affine type <i>A </i>and Ariki’s theorem -- Decomposition numbers for exceptional types.</p>.
Physical Description:
XII, 401p. 6 illus. digital.
Electronic Location:
http://dx.doi.org/10.1007/978-0-85729-716-7
Publication Date:
2011.
Title:
Group Identities on Units and Symmetric Units of Group Rings by Gregory T. Lee.
Algebra and Applications ;
Algebra and Applications ;
Author:
Lee, Gregory T.
SpringerLink (Online service)
General Notes:
<p>Group Identities on Units of Group Rings -- Group Identities on Symmetric Units -- Lie Identities on Symmetric Elements -- Nilpotence of U(FG) and U+(FG) -- The Bounded Engel Property -- Solvability of U(FG) and U+(FG) -- Further Reading -- Some Results on Prime and Semiprime Rings</p>.
<p>Let FG be the group ring of a group G over a field F. Write U(FG) for the group of units of FG. It is an important problem to determine the conditions under which U(FG) satisfies a group identity. In the mid 1990s, a conjecture of Hartley was verified, namely, if U(FG) satisfies a group identity, and G is torsion, then FG satisfies a polynomial identity. Necessary and sufficient conditions for U(FG) to satisfy a group identity soon followed.</p> <p>Since the late 1990s, many papers have been devoted to the study of the symmetric units; that is, those units u satisfying u* = u, where * is the involution on FG defined by sending each element of G to its inverse. The conditions under which these symmetric units satisfy a group identity have now been determined.</p> <p>This book presents these results for arbitrary group identities, as well as the conditions under which the unit group or the set of symmetric units satisfies several particular group identities of interest.</p>
Publisher:
Springer London,
Publication Place:
London :
ISBN:
9781849965040
Subject:
Mathematics.
Algebra.
Group theory.
Mathematics.
Associative Rings and Algebras.
Group Theory and Generalizations.
Series:
Algebra and Applications ; 12
Algebra and Applications ; 12
Contents:
<p>Group Identities on Units of Group Rings -- Group Identities on Symmetric Units -- Lie Identities on Symmetric Elements -- Nilpotence of U(FG) and U+(FG) -- The Bounded Engel Property -- Solvability of U(FG) and U+(FG) -- Further Reading -- Some Results on Prime and Semiprime Rings</p>.
Physical Description:
XII, 196 p. digital.
Electronic Location:
http://dx.doi.org/10.1007/978-1-84996-504-0
Publication Date:
2010.
Title:
Group Identities on Units and Symmetric Units of Group Rings by Gregory T. Lee.
Algebra and Applications ;
Algebra and Applications ;
Author:
Lee, Gregory T.
SpringerLink (Online service)
General Notes:
<p>Group Identities on Units of Group Rings -- Group Identities on Symmetric Units -- Lie Identities on Symmetric Elements -- Nilpotence of U(FG) and U+(FG) -- The Bounded Engel Property -- Solvability of U(FG) and U+(FG) -- Further Reading -- Some Results on Prime and Semiprime Rings</p>.
<p>Let FG be the group ring of a group G over a field F. Write U(FG) for the group of units of FG. It is an important problem to determine the conditions under which U(FG) satisfies a group identity. In the mid 1990s, a conjecture of Hartley was verified, namely, if U(FG) satisfies a group identity, and G is torsion, then FG satisfies a polynomial identity. Necessary and sufficient conditions for U(FG) to satisfy a group identity soon followed.</p> <p>Since the late 1990s, many papers have been devoted to the study of the symmetric units; that is, those units u satisfying u* = u, where * is the involution on FG defined by sending each element of G to its inverse. The conditions under which these symmetric units satisfy a group identity have now been determined.</p> <p>This book presents these results for arbitrary group identities, as well as the conditions under which the unit group or the set of symmetric units satisfies several particular group identities of interest.</p>
Publisher:
Springer London,
Publication Place:
London :
ISBN:
9781849965040
Subject:
Mathematics.
Algebra.
Group theory.
Mathematics.
Associative Rings and Algebras.
Group Theory and Generalizations.
Series:
Algebra and Applications ; 12
Algebra and Applications ; 12
Contents:
<p>Group Identities on Units of Group Rings -- Group Identities on Symmetric Units -- Lie Identities on Symmetric Elements -- Nilpotence of U(FG) and U+(FG) -- The Bounded Engel Property -- Solvability of U(FG) and U+(FG) -- Further Reading -- Some Results on Prime and Semiprime Rings</p>.
Physical Description:
XII, 196 p. digital.
Electronic Location:
http://dx.doi.org/10.1007/978-1-84996-504-0
Publication Date:
2010.
Title:
Group and Ring Theoretic Properties of Polycyclic Groups by B.A.F. Wehrfritz.
Algebra and Applications ;
Algebra and Applications ;
Author:
Wehrfritz, B.A.F.
SpringerLink (Online service)
General Notes:
<P>Foreword -- Some basic group theory -- Some ring theory -- Soluble linear groups -- Further group-theoretic properties of polycyclic groups -- Groups acting on finitely generated commutative rings -- Prime ideals in polycyclic-group rings -- The structure of modules over polycyclic groups -- Semilinear and skew linear groups.</P>.
<P>Polycyclic groups are built from cyclic groups in a specific way. They arise in many contexts within group theory itself but also more generally in algebra, for example in the theory of Noetherian rings. They also touch on some aspects of topology, geometry and number theory. The first half of this book develops the standard group theoretic techniques for studying polycyclic groups and the basic properties of these groups. The second half then focuses specifically on the ring theoretic properties of polycyclic groups and their applications, often to purely group theoretic situations.</P> <P>The book is not intended to be encyclopedic. Instead, it is a study manual for graduate students and researchers coming into contact with polycyclic groups, where the main lines of the subject can be learned from scratch by any reader who has been exposed to some undergraduate algebra, especially groups, rings and vector spaces. Thus the book has been kept short and readable with a view that it can be read and worked through from cover to cover. At the end of each topic covered there is a description without proofs, but with full references, of further developments in the area. The book then concludes with an extensive bibliography of items relating to polycyclic groups.</P> <P></P>
Publisher:
Springer London,
Publication Place:
London :
ISBN:
9781848829411
Subject:
Mathematics.
Algebra.
Group theory.
Mathematics.
Group Theory and Generalizations.
Associative Rings and Algebras.
Commutative Rings and Algebras.
Series:
Algebra and Applications ; 10
Algebra and Applications ; 10
Contents:
<P>Foreword -- Some basic group theory -- Some ring theory -- Soluble linear groups -- Further group-theoretic properties of polycyclic groups -- Groups acting on finitely generated commutative rings -- Prime ideals in polycyclic-group rings -- The structure of modules over polycyclic groups -- Semilinear and skew linear groups.</P>.
Physical Description:
digital.
Electronic Location:
http://dx.doi.org/10.1007/978-1-84882-941-1
Publication Date:
2009.
Title:
Group and Ring Theoretic Properties of Polycyclic Groups by B.A.F. Wehrfritz.
Algebra and Applications ;
Algebra and Applications ;
Author:
Wehrfritz, B.A.F.
SpringerLink (Online service)
General Notes:
<P>Foreword -- Some basic group theory -- Some ring theory -- Soluble linear groups -- Further group-theoretic properties of polycyclic groups -- Groups acting on finitely generated commutative rings -- Prime ideals in polycyclic-group rings -- The structure of modules over polycyclic groups -- Semilinear and skew linear groups.</P>.
<P>Polycyclic groups are built from cyclic groups in a specific way. They arise in many contexts within group theory itself but also more generally in algebra, for example in the theory of Noetherian rings. They also touch on some aspects of topology, geometry and number theory. The first half of this book develops the standard group theoretic techniques for studying polycyclic groups and the basic properties of these groups. The second half then focuses specifically on the ring theoretic properties of polycyclic groups and their applications, often to purely group theoretic situations.</P> <P>The book is not intended to be encyclopedic. Instead, it is a study manual for graduate students and researchers coming into contact with polycyclic groups, where the main lines of the subject can be learned from scratch by any reader who has been exposed to some undergraduate algebra, especially groups, rings and vector spaces. Thus the book has been kept short and readable with a view that it can be read and worked through from cover to cover. At the end of each topic covered there is a description without proofs, but with full references, of further developments in the area. The book then concludes with an extensive bibliography of items relating to polycyclic groups.</P> <P></P>
Publisher:
Springer London,
Publication Place:
London :
ISBN:
9781848829411
Subject:
Mathematics.
Algebra.
Group theory.
Mathematics.
Group Theory and Generalizations.
Associative Rings and Algebras.
Commutative Rings and Algebras.
Series:
Algebra and Applications ; 10
Algebra and Applications ; 10
Contents:
<P>Foreword -- Some basic group theory -- Some ring theory -- Soluble linear groups -- Further group-theoretic properties of polycyclic groups -- Groups acting on finitely generated commutative rings -- Prime ideals in polycyclic-group rings -- The structure of modules over polycyclic groups -- Semilinear and skew linear groups.</P>.
Physical Description:
digital.
Electronic Location:
http://dx.doi.org/10.1007/978-1-84882-941-1
Publication Date:
2009.
Title:
Specialization of Quadratic and Symmetric Bilinear Forms by Manfred Knebusch.
Algebra and Applications ;
Algebra and Applications ;
Author:
Knebusch, Manfred.
SpringerLink (Online service)
General Notes:
Fundamentals of Specialization Theory -- Generic Splitting Theory -- Some Applications -- Specialization with Respect to Quadratic Places -- Forms -- References -- Index.
The specialization theory of quadratic and symmetric bilinear forms over fields and the subsequent generic splitting theory of quadratic forms were invented by the author in the mid-1970's. They came to fruition in the ensuing decades and have become an integral part of the geometric methods in quadratic form theory. This book comprehensively covers the specialization and generic splitting theories. These theories, originally developed mainly for fields of characteristic different from 2, are explored here without this restriction. In this book, a quadratic form φ over a field of characteristic 2 is allowed to have a big quasilinear part QL(φ) (defined as the restriction of φ to the radical of the bilinear form associated to φ), while in most of the literature QL(φ) is assumed to have dimension at most 1. Of course, in nature, quadratic forms with a big quasilinear part abound. In addition to chapters on specialization theory, generic splitting theory and their applications, the book's final chapter contains research never before published on specialization with respect to quadratic places and will provide the reader with a glimpse towards the future.
Publisher:
Springer London,
Publication Place:
London :
ISBN:
9781848822429
Subject:
Mathematics.
Algebra.
Mathematics.
Algebra.
Series:
Algebra and Applications ; 11
Algebra and Applications ; 11
Contents:
Fundamentals of Specialization Theory -- Generic Splitting Theory -- Some Applications -- Specialization with Respect to Quadratic Places -- Forms -- References -- Index.
Physical Description:
XIV, 194 p. digital.
Electronic Location:
http://dx.doi.org/10.1007/978-1-84882-242-9
Publication Date:
2010.
Title:
Specialization of Quadratic and Symmetric Bilinear Forms by Manfred Knebusch.
Algebra and Applications ;
Algebra and Applications ;
Author:
Knebusch, Manfred.
SpringerLink (Online service)
General Notes:
Fundamentals of Specialization Theory -- Generic Splitting Theory -- Some Applications -- Specialization with Respect to Quadratic Places -- Forms -- References -- Index.
The specialization theory of quadratic and symmetric bilinear forms over fields and the subsequent generic splitting theory of quadratic forms were invented by the author in the mid-1970's. They came to fruition in the ensuing decades and have become an integral part of the geometric methods in quadratic form theory. This book comprehensively covers the specialization and generic splitting theories. These theories, originally developed mainly for fields of characteristic different from 2, are explored here without this restriction. In this book, a quadratic form φ over a field of characteristic 2 is allowed to have a big quasilinear part QL(φ) (defined as the restriction of φ to the radical of the bilinear form associated to φ), while in most of the literature QL(φ) is assumed to have dimension at most 1. Of course, in nature, quadratic forms with a big quasilinear part abound. In addition to chapters on specialization theory, generic splitting theory and their applications, the book's final chapter contains research never before published on specialization with respect to quadratic places and will provide the reader with a glimpse towards the future.
Publisher:
Springer London,
Publication Place:
London :
ISBN:
9781848822429
Subject:
Mathematics.
Algebra.
Mathematics.
Algebra.
Series:
Algebra and Applications ; 11
Algebra and Applications ; 11
Contents:
Fundamentals of Specialization Theory -- Generic Splitting Theory -- Some Applications -- Specialization with Respect to Quadratic Places -- Forms -- References -- Index.
Physical Description:
XIV, 194 p. digital.
Electronic Location:
http://dx.doi.org/10.1007/978-1-84882-242-9
Publication Date:
2010.
Title:
Classical Finite Transformation Semigroups An Introduction / by Olexandr Ganyushkin, Volodymyr Mazorchuk.
Algebra and Applications ;
Algebra and Applications ;
Author:
Ganyushkin, Olexandr.
Mazorchuk, Volodymyr.
SpringerLink (Online service)
General Notes:
Preface -- 1. Ordinary and partial transformations -- 2. The semigroups Tn, PT n and ISn -- 3. Generating Systems -- 4. Ideals and Green's relations -- 5. Subgroups and subsemigroups -- 6. Other relations on semigroups -- 7. Endomorphisms -- 8. Nilpotent subsemigroups -- 9. Presentation -- 10. Transitive actions -- 11. Linear representations -- 12. Cross-sections -- 13. Variants -- 14. Order-related subsemigroups -- Answers and hints to exercises -- Bibliography -- List of notation -- Index.
<P>The aim of this monograph is to give a self-contained introduction to the modern theory of finite transformation semigroups with a strong emphasis on concrete examples and combinatorial applications. It covers the following topics on the examples of the three classical finite transformation semigroups: transformations and semigroups, ideals and Green's relations, subsemigroups, congruences, endomorphisms, nilpotent subsemigroups, presentations, actions on sets, linear representations, cross-sections and variants. The book contains many exercises and historical comments and is directed, first of all, to both graduate and postgraduate students looking for an introduction to the theory of transformation semigroups, but should also prove useful to tutors and researchers.</P>
Publisher:
Springer London,
Publication Place:
London :
ISBN:
9781848002814
Subject:
Mathematics.
Group theory.
Combinatorics.
Mathematics.
Group Theory and Generalizations.
Combinatorics.
Series:
Algebra and Applications ; 9
Algebra and Applications ; 9
Contents:
Preface -- 1. Ordinary and partial transformations -- 2. The semigroups Tn, PT n and ISn -- 3. Generating Systems -- 4. Ideals and Green's relations -- 5. Subgroups and subsemigroups -- 6. Other relations on semigroups -- 7. Endomorphisms -- 8. Nilpotent subsemigroups -- 9. Presentation -- 10. Transitive actions -- 11. Linear representations -- 12. Cross-sections -- 13. Variants -- 14. Order-related subsemigroups -- Answers and hints to exercises -- Bibliography -- List of notation -- Index.
Physical Description:
digital.
Electronic Location:
http://dx.doi.org/10.1007/978-1-84800-281-4
Publication Date:
2009.
Title:
Classical Finite Transformation Semigroups An Introduction / by Olexandr Ganyushkin, Volodymyr Mazorchuk.
Algebra and Applications ;
Algebra and Applications ;
Author:
Ganyushkin, Olexandr.
Mazorchuk, Volodymyr.
SpringerLink (Online service)
General Notes:
Preface -- 1. Ordinary and partial transformations -- 2. The semigroups Tn, PT n and ISn -- 3. Generating Systems -- 4. Ideals and Green's relations -- 5. Subgroups and subsemigroups -- 6. Other relations on semigroups -- 7. Endomorphisms -- 8. Nilpotent subsemigroups -- 9. Presentation -- 10. Transitive actions -- 11. Linear representations -- 12. Cross-sections -- 13. Variants -- 14. Order-related subsemigroups -- Answers and hints to exercises -- Bibliography -- List of notation -- Index.
<P>The aim of this monograph is to give a self-contained introduction to the modern theory of finite transformation semigroups with a strong emphasis on concrete examples and combinatorial applications. It covers the following topics on the examples of the three classical finite transformation semigroups: transformations and semigroups, ideals and Green's relations, subsemigroups, congruences, endomorphisms, nilpotent subsemigroups, presentations, actions on sets, linear representations, cross-sections and variants. The book contains many exercises and historical comments and is directed, first of all, to both graduate and postgraduate students looking for an introduction to the theory of transformation semigroups, but should also prove useful to tutors and researchers.</P>
Publisher:
Springer London,
Publication Place:
London :
ISBN:
9781848002814
Subject:
Mathematics.
Group theory.
Combinatorics.
Mathematics.
Group Theory and Generalizations.
Combinatorics.
Series:
Algebra and Applications ; 9
Algebra and Applications ; 9
Contents:
Preface -- 1. Ordinary and partial transformations -- 2. The semigroups Tn, PT n and ISn -- 3. Generating Systems -- 4. Ideals and Green's relations -- 5. Subgroups and subsemigroups -- 6. Other relations on semigroups -- 7. Endomorphisms -- 8. Nilpotent subsemigroups -- 9. Presentation -- 10. Transitive actions -- 11. Linear representations -- 12. Cross-sections -- 13. Variants -- 14. Order-related subsemigroups -- Answers and hints to exercises -- Bibliography -- List of notation -- Index.
Physical Description:
digital.
Electronic Location:
http://dx.doi.org/10.1007/978-1-84800-281-4
Publication Date:
2009.
Title:
Algebra and Coalgebra in Computer Science 5th International Conference, CALCO 2013, Warsaw, Poland, September 3-6, 2013. Proceedings / edited by Reiko Heckel, Stefan Milius.
Lecture Notes in Computer Science,
Lecture notes in computer science,
Author:
Heckel, Reiko. editor.
Milius, Stefan. editor.
SpringerLink (Online service)
General Notes:
Invited Talks -- An Effect System for Algebraic Effects and Handlers -- Automata and Algebras for Infinite Words and Trees -- Positive Inductive-Recursive Definitions -- Coalgebraic up-to techniques -- Contributed Papers -- Exploiting Algebraic Laws to Improve Mechanized Axiomatization -- Positive Fragments of Coalgebraic Logics -- Many-valued Relation Lifting and Moss' Coalgebraic Logic -- Saturated Semantics for Coalgebraic Logic Programming -- Presenting Distributive Laws -- Interaction and observation: categorical semantics of reactive systems trough dialgebras -- Homomorphisms of coalgebras from predicate liftings -- From Kleisli Categories to Commutative C*-algebras: Probabilistic Gelfand Duality -- Trace Semantics via Generic Observations -- Full abstraction for fair testing in CCS -- A simple case of rationality of escalation -- Coalgebras with Symmetries and Modelling Quantum Systems -- From Operational Chu Duality to Coalgebraic Quantum Symmetry -- Noninterfering Schedulers|When Possibilistic Noninterference Implies Probabilistic Noninterference -- Simulations and Bisimulations For Coalgebraic Modal Logics -- A Coalgebraic View of "-Transitions -- Nets, relations and linking diagrams -- A Logic-Programming Semantics of Services -- CALCO-Tools Workshop -- Preface to CALCO-Tools -- Checking Conservativity With Hets -- The HI-Maude Tool -- Constructor-based Inductive Theorem Prover -- A Timed CTL Model Checker for Real-Time Maude -- Hybridisation at Work -- Penrose: Putting Compositionality to Work For Petri Net Reachability -- QStream: A Suite of Streams.
This book constitutes the refereed proceedings of the 5th International Conference on Algebra and Coalgebra in Computer Science, CALCO 2013, held in Warsaw, Poland, in September 2013. The 18 full papers presented together with 4 invited talks were carefully reviewed and selected from 33 submissions. The papers cover topics in the fields of abstract models and logics, specialized models and calculi, algebraic and coalgebraic semantics, system specification and verification, as well as corecursion in programming languages, and algebra and coalgebra in quantum computing. The book also includes 6 papers from the CALCO Tools Workshop, co-located with CALCO 2013 and dedicated to tools based on algebraic and/or coalgebraic principles.
Publisher:
Springer Berlin Heidelberg : Imprint: Springer,
Publication Place:
Berlin, Heidelberg :
ISBN:
9783642402067
Subject:
Computer science.
Software engineering.
Information theory.
Algebra -- Data processing.
Computer science.
Theory of Computation.
Software engineering.
Quantum Computing.
Symbolic and Algebraic Manipulation.
Series:
Lecture Notes in Computer Science, 8089
Lecture notes in computer science, 8089
Contents:
Invited Talks -- An Effect System for Algebraic Effects and Handlers -- Automata and Algebras for Infinite Words and Trees -- Positive Inductive-Recursive Definitions -- Coalgebraic up-to techniques -- Contributed Papers -- Exploiting Algebraic Laws to Improve Mechanized Axiomatization -- Positive Fragments of Coalgebraic Logics -- Many-valued Relation Lifting and Moss' Coalgebraic Logic -- Saturated Semantics for Coalgebraic Logic Programming -- Presenting Distributive Laws -- Interaction and observation: categorical semantics of reactive systems trough dialgebras -- Homomorphisms of coalgebras from predicate liftings -- From Kleisli Categories to Commutative C*-algebras: Probabilistic Gelfand Duality -- Trace Semantics via Generic Observations -- Full abstraction for fair testing in CCS -- A simple case of rationality of escalation -- Coalgebras with Symmetries and Modelling Quantum Systems -- From Operational Chu Duality to Coalgebraic Quantum Symmetry -- Noninterfering Schedulers|When Possibilistic Noninterference Implies Probabilistic Noninterference -- Simulations and Bisimulations For Coalgebraic Modal Logics -- A Coalgebraic View of "-Transitions -- Nets, relations and linking diagrams -- A Logic-Programming Semantics of Services -- CALCO-Tools Workshop -- Preface to CALCO-Tools -- Checking Conservativity With Hets -- The HI-Maude Tool -- Constructor-based Inductive Theorem Prover -- A Timed CTL Model Checker for Real-Time Maude -- Hybridisation at Work -- Penrose: Putting Compositionality to Work For Petri Net Reachability -- QStream: A Suite of Streams.
Physical Description:
XIV, 359 p. 29 illus. online resource.
Electronic Location:
http://dx.doi.org/10.1007/978-3-642-40206-7
Publication Date:
2013.
Title:
Algebra and its Applications ICAA, Aligarh, India, December 2014 / edited by Syed Tariq Rizvi, Asma Ali, Vincenzo De Filippis.
Springer Proceedings in Mathematics & Statistics,
Springer Proceedings in Mathematics & Statistics,
Author:
Rizvi, Syed Tariq. editor.
Ali, Asma. editor.
Filippis, Vincenzo De. editor.
SpringerLink (Online service)
General Notes:
Jae Koel Park and S. M. Tariq Rizvi: On some Classes of Module Hulls -- Akihiro Yamamura: Spined Product Decompositions of Orthocryptogroups -- Vincenzo de Filippis: Generalized Skew Derivations and g-Lie Derivations of Prime Rings -- Ashish Kumar Srivastava: Additive Representations of Elements in Rings: A Survey -- Shuliang Huang: Notes on Commutativity of Prime Rings -- Shervin Sahebi and V. Rahmani: Generalized Derivations on Rings and Banach Algebras -- Ravi A. Rao: A study of Suslin Matrices: Their Properties and Uses -- Shreedevi K. Masuti, Parangama Sarkar and J. K. Verma: Variation on the Grothendieck-Serre Formula for Hilbert Functions and Their Applications -- Tony Joseph Puthenpurakal: De Rham Cohomology of Local Cohomology Modules -- Manoj Kumar Yadav: Central Quotient Versus Commutator Subgroup of Groups -- Tamilselvi, A. Vidhya and B. Kethesan: Robinson-Schensted Correspondence for the Walled Brauer Algebras and the Walled Signed Brauer algebras -- M.K. Sen: Ó¶- Semigroups: A Survey -- N. K. Thakare, B. N. Waphare and AvinashPatil: Comparability Axioms in Orthomodular Lattices and Rings with Involution -- A. R. Rajan: Structure theory of regular Semigroups using Categories -- P. G. Romeo and Akhila R.: Biorder Ideals and Regular Rings -- Asma Ali and Farhat Ali: Product of Generalized Semiderivation in Prime Near Rings -- Selvaraj and R. Saravanan: n-Strongly Gorenstein Projective and Injective Complexes -- Basudeb Dhara: Generalized Derivations with Nilpotent Values on Multilinear Polynomials in Prime Rings -- Manoj Kumar Patel: Properties of Semi-Projective Modules and Their Endomorphism Rings -- R. P. Sharma: L Labelling of Sets Under the Actions of Sn and An -- Anil Khainar and B. N. Waphare: Zero-Divisor Graphs of Laurent Polynomials and Laurent Power Series -- Basudeb Dhara, Asma Ali and Shahoor Khan: Pair of Generalized Derivations and Lie Ideals in Prime Rings -- T. Tamizh Chelvam, T. Asir and K. Selvakumar: On Domination in Graphs from Commutative Rings: A survey -- A. K. Chaturvedi: On Iso-Retractable Modules and Rings -- Azeef Muhammed P. A.: Normal Categories from Completely Simple Semigroups -- N. M. Khan and Mohd. Aasim Khan: Ordered Semigroups Characterize in Terms of Intuitionstic Fuzzy Ideals -- R. D. Giri: On a Problem of Satyanarayana Regarding the Recognizability of Codes.
This book discusses recent developments and the latest research in algebra and related topics. The book allows aspiring researchers to update their understanding of prime rings, generalized derivations, generalized semiderivations, regular semigroups, completely simple semigroups, module hulls, injective hulls, Baer modules, extending modules, local cohomology modules, orthogonal lattices, Banach algebras, multilinear polynomials, fuzzy ideals, Laurent power series, and Hilbert functions. All the contributing authors are leading international academicians and researchers in their respective fields. Most of the papers were presented at the international conference on Algebra and its Applications (ICAA-2014), held at Aligarh Muslim University, India, from December 15–17, 2014. The conference has emerged as a powerful forum offering researchers a venue to meet and discuss advances in algebra and its applications, inspiring further research directions. <.
Publisher:
Springer Singapore : Imprint: Springer,
Publication Place:
Singapore :
ISBN:
9789811016516
Subject:
Mathematics.
Algebra.
Sequences (Mathematics).
Graph theory.
Mathematics.
Algebra.
Sequences, Series, Summability.
Graph theory.
Series:
Springer Proceedings in Mathematics & Statistics, 174
Springer Proceedings in Mathematics & Statistics, 174
Contents:
Jae Koel Park and S. M. Tariq Rizvi: On some Classes of Module Hulls -- Akihiro Yamamura: Spined Product Decompositions of Orthocryptogroups -- Vincenzo de Filippis: Generalized Skew Derivations and g-Lie Derivations of Prime Rings -- Ashish Kumar Srivastava: Additive Representations of Elements in Rings: A Survey -- Shuliang Huang: Notes on Commutativity of Prime Rings -- Shervin Sahebi and V. Rahmani: Generalized Derivations on Rings and Banach Algebras -- Ravi A. Rao: A study of Suslin Matrices: Their Properties and Uses -- Shreedevi K. Masuti, Parangama Sarkar and J. K. Verma: Variation on the Grothendieck-Serre Formula for Hilbert Functions and Their Applications -- Tony Joseph Puthenpurakal: De Rham Cohomology of Local Cohomology Modules -- Manoj Kumar Yadav: Central Quotient Versus Commutator Subgroup of Groups -- Tamilselvi, A. Vidhya and B. Kethesan: Robinson-Schensted Correspondence for the Walled Brauer Algebras and the Walled Signed Brauer algebras -- M.K. Sen: Ó¶- Semigroups: A Survey -- N. K. Thakare, B. N. Waphare and AvinashPatil: Comparability Axioms in Orthomodular Lattices and Rings with Involution -- A. R. Rajan: Structure theory of regular Semigroups using Categories -- P. G. Romeo and Akhila R.: Biorder Ideals and Regular Rings -- Asma Ali and Farhat Ali: Product of Generalized Semiderivation in Prime Near Rings -- Selvaraj and R. Saravanan: n-Strongly Gorenstein Projective and Injective Complexes -- Basudeb Dhara: Generalized Derivations with Nilpotent Values on Multilinear Polynomials in Prime Rings -- Manoj Kumar Patel: Properties of Semi-Projective Modules and Their Endomorphism Rings -- R. P. Sharma: L Labelling of Sets Under the Actions of Sn and An -- Anil Khainar and B. N. Waphare: Zero-Divisor Graphs of Laurent Polynomials and Laurent Power Series -- Basudeb Dhara, Asma Ali and Shahoor Khan: Pair of Generalized Derivations and Lie Ideals in Prime Rings -- T. Tamizh Chelvam, T. Asir and K. Selvakumar: On Domination in Graphs from Commutative Rings: A survey -- A. K. Chaturvedi: On Iso-Retractable Modules and Rings -- Azeef Muhammed P. A.: Normal Categories from Completely Simple Semigroups -- N. M. Khan and Mohd. Aasim Khan: Ordered Semigroups Characterize in Terms of Intuitionstic Fuzzy Ideals -- R. D. Giri: On a Problem of Satyanarayana Regarding the Recognizability of Codes.
Physical Description:
XVI, 430 p. online resource.
Electronic Location:
http://dx.doi.org/10.1007/978-981-10-1651-6
Publication Date:
2016.
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