Unit Groups Of Group Rings
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Unit Groups Of Group Rings
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Author : Gregory Karpilovsky
language : en
Publisher: Longman Scientific and Technical
Release Date : 1989
Unit Groups Of Group Rings written by Gregory Karpilovsky and has been published by Longman Scientific and Technical this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
Group Identities On Units And Symmetric Units Of Group Rings
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Author : Gregory T Lee
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-19
Group Identities On Units And Symmetric Units Of Group Rings written by Gregory T Lee and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-19 with Mathematics categories.
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. 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. 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.
Structure Theorems Of Unit Groups
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Author : Eric Jespers
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2015-11-13
Structure Theorems Of Unit Groups written by Eric Jespers and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-13 with Mathematics categories.
This two-volume graduate textbook gives a comprehensive, state-of-the-art account of describing large subgroups of the unit group of the integral group ring of a finite group and, more generally, of the unit group of an order in a finite dimensional semisimple rational algebra. Since the book is addressed to graduate students as well as young researchers, all required background on these diverse areas, both old and new, is included. Supporting problems illustrate the results and complete some of the proofs. Volume 1 contains all the details on describing generic constructions of units and the subgroup they generate. Volume 2 mainly is about structure theorems and geometric methods. Without being encyclopaedic, all main results and techniques used to achieve these results are included. Basic courses in group theory, ring theory and field theory are assumed as background.
The Algebraic Structure Of Group Rings
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Author : Donald S. Passman
language : en
Publisher: Courier Corporation
Release Date : 2011-01-01
The Algebraic Structure Of Group Rings written by Donald S. Passman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-01 with Mathematics categories.
"'Highly recommended' by the Bulletin of the London Mathematical Society, this book offers a comprehensive, self-contained treatment of group rings. The subject involves the intersection of two essentially different disciplines, group theory and ring theory. The Bulletin of the American Mathematical Society hailed this treatment as 'a majestic account,' proclaiming it "encyclopedic and lucid." 1985 edition"--
Units In Integral Group Rings
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Author : Sudarshan K. Sehgal
language : en
Publisher: Halsted Press
Release Date : 1993-10-01
Units In Integral Group Rings written by Sudarshan K. Sehgal and has been published by Halsted Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-10-01 with categories.
Topics In Group Rings
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Author : Sudarshan K. Sehgal
language : en
Publisher:
Release Date : 1978
Topics In Group Rings written by Sudarshan K. Sehgal and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Mathematics categories.
The group ring KG of the group G over a commutative unital ring K comprises an attractive object of study. This is one of the few algebraic structures that allow for explicit computations. Several easily formulated questions are associated with this topic. Many interesting results have been obtained in this area by using deep results and techniques from group theory, ring theory, and number theory. Most of the results presented and techniques used have a number theoretic flavor. Aimed at advanced graduate students and research mathematicians in algebra.
A Course In Finite Group Representation Theory
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Author : Peter Webb
language : en
Publisher: Cambridge University Press
Release Date : 2016-08-19
A Course In Finite Group Representation Theory written by Peter Webb and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-19 with Mathematics categories.
This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.
Groups Rings And Group Rings
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Author : A. Giambruno
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Groups Rings And Group Rings written by A. Giambruno and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
Represents the proceedings of the conference on Groups, Rings and Group Rings, held July 28 - August 2, 2008, in Ubatuba, Brazil. This title contains results in active research areas in the theory of groups, group rings and algebras (including noncommutative rings), polynomial identities, Lie algebras and superalgebras.
Integral Closure Of Ideals Rings And Modules
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Author : Craig Huneke
language : en
Publisher: Cambridge University Press
Release Date : 2006-10-12
Integral Closure Of Ideals Rings And Modules written by Craig Huneke and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-12 with Mathematics categories.
Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.
Representations Of Algebraic Groups
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Author : Jens Carsten Jantzen
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Representations Of Algebraic Groups written by Jens Carsten Jantzen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Gives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.