Infinite Group Rings
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Infinite Group Rings
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Author : Donald S. Passman
language : en
Publisher:
Release Date : 1971
Infinite Group Rings written by Donald S. Passman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Mathematics categories.
The algebraic study of group rings was initiated in 1949 by I. Kaplansky. The subject has been pursued by a small but growing number of researchers, and has reached a point in its development where a coherent account of the basic results is needed. That is the goal of this text. The topics covered are selective, with material balanced between ring theory and group theory, and a basic one year course in algebra should provide sufficient background for readers.
Infinite Group Theory From The Past To The Future
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Author : Paul Baginski
language : en
Publisher: World Scientific
Release Date : 2017-12-26
Infinite Group Theory From The Past To The Future written by Paul Baginski and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-26 with Mathematics categories.
The development of algebraic geometry over groups, geometric group theory and group-based cryptography, has led to there being a tremendous recent interest in infinite group theory. This volume presents a good collection of papers detailing areas of current interest.
Artinian Modules Over Group Rings
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Author : Leonid Kurdachenko
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-12-22
Artinian Modules Over Group Rings written by Leonid Kurdachenko 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 2006-12-22 with Mathematics categories.
This book highlights important developments on artinian modules over group rings of generalized nilpotent groups. Along with traditional topics such as direct decompositions of artinian modules, criteria of complementability for some important modules, and criteria of semisimplicity of artinian modules, it also focuses on recent advanced results on these matters.
Group Rings And Class Groups
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Author : K.W. Roggenkamp
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Group Rings And Class Groups written by K.W. Roggenkamp and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The first part of the book centers around the isomorphism problem for finite groups; i.e. which properties of the finite group G can be determined by the integral group ring ZZG ? The authors have tried to present the results more or less selfcontained and in as much generality as possible concerning the ring of coefficients. In the first section, the class sum correspondence and some related results are derived. This part is the proof of the subgroup rigidity theorem (Scott - Roggenkamp; Weiss) which says that a finite subgroup of the p-adic integral group ring of a finite p-group is conjugate to a subgroup of the finite group. A counterexample to the conjecture of Zassenhaus that group basis are rationally conjugate, is presented in the semilocal situation (Scott - Roggenkamp). To this end, an extended version of Clifford theory for p-adic integral group rings is presented. Moreover, several examples are given to demonstrate the complexity of the isomorphism problem. The second part of the book is concerned with various aspects of the structure of rings of integers as Galois modules. It begins with a brief overview of major results in the area; thereafter the majority of the text focuses on the use of the theory of Hopf algebras. It begins with a thorough and detailed treatment of the required foundational material and concludes with new and interesting applications to cyclotomic theory and to elliptic curves with complex multiplication. Examples are used throughout both for motivation, and also to illustrate new ideas.
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"--
Groups Rings And Algebras
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Author : Donald S. Passman
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Groups Rings And Algebras written by Donald S. Passman 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 2006 with Mathematics categories.
This is a companion volume to the conference in honor of Donald S. Passman held in Madison, Wisconsin in June 2005. It contains research papers on Algebras, Group Rings, Hopf Algebras, Invariant Theory, Lie Algebras and their Enveloping Algebras, Noncommutative Algebraic Geometry, Noncommutative Rings, and other topics. The papers represent an important part of the latest research in these areas.
An Introduction To Group Rings
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Author : César Polcino Milies
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-01-31
An Introduction To Group Rings written by César Polcino Milies 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 2002-01-31 with Mathematics categories.
to Group Rings by Cesar Polcino Milies Instituto de Matematica e Estatistica, Universidade de sao Paulo, sao Paulo, Brasil and Sudarshan K. Sehgal Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton. Canada SPRINGER-SCIENCE+BUSINESS MEDIA, B.V. A c.I.P. Catalogue record for this book is available from the Library of Congress. ISBN 978-1-4020-0239-7 ISBN 978-94-010-0405-3 (eBook) DOI 10.1007/978-94-010-0405-3 Printed an acid-free paper AII Rights Reserved (c) 2002 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2002 Softcover reprint ofthe hardcover Ist edition 2002 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, inc1uding photocopying, recording Of by any information storage and retrieval system, without written permis sion from the copyright owner. Contents Preface ix 1 Groups 1 1.1 Basic Concepts . . . . . . . . . . . . 1 1.2 Homomorphisms and Factor Groups 10 1.3 Abelian Groups . 18 1.4 Group Actions, p-groups and Sylow Subgroups 21 1.5 Solvable and Nilpotent Groups 27 1.6 FC Groups .
Ring Constructions And Applications
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Author : Andrei V. Kelarev
language : en
Publisher: World Scientific
Release Date : 2002
Ring Constructions And Applications written by Andrei V. Kelarev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
This book contains the definitions of several ring constructions used in various applications. The concept of a groupoid-graded ring includes many of these constructions as special cases and makes it possible to unify the exposition. Recent research results on groupoid-graded rings and more specialized constructions are presented. In addition, there is a chapter containing open problems currently considered in the literature. Ring Constructions and Applications can serve as an excellent introduction for graduate students to many ring constructions as well as to essential basic concepts of group, semigroup and ring theories used in proofs.
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.
Groups Rings Modules
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Author : Maurice Auslander
language : en
Publisher: Courier Corporation
Release Date : 2014-06-18
Groups Rings Modules written by Maurice Auslander and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-18 with Mathematics categories.
This classic monograph is geared toward advanced undergraduates and graduate students. The treatment presupposes some familiarity with sets, groups, rings, and vector spaces. The four-part approach begins with examinations of sets and maps, monoids and groups, categories, and rings. The second part explores unique factorization domains, general module theory, semisimple rings and modules, and Artinian rings. Part three's topics include localization and tensor products, principal ideal domains, and applications of fundamental theorem. The fourth and final part covers algebraic field extensions and Dedekind domains. Exercises are provided at the end of each chapter. Dover (2014) republication of the edition originally published by Harper & Row Publishers, New York, 1974. See every Dover book in print at www.doverpublications.com