Groups, Rings, Group Rings, and Hopf Algebras

Author: Jeffrey Bergen,Stefan Catoiu,William Chin

Publisher: American Mathematical Soc.

ISBN: 1470428059

Category: Associative rings and algebras -- Modules, bimodules and ideals -- Modules, bimodules and ideals

Page: 277

View: 6023

This volume contains the proceedings of the International Conference on Groups, Rings, Group Rings, and Hopf Algebras, held October 2–4, 2015 at Loyola University, Chicago, IL, and the AMS Special Session on Groups, Rings, Group Rings, and Hopf Algebras, held October 3–4, 2015, at Loyola University, Chicago, IL. Both conferences were held in honor of Donald S. Passman's 75th Birthday. Centered in the area of group rings and algebras, this volume contains a mixture of cutting edge research topics in group theory, ring theory, algebras and their representations, Hopf algebras and quantum groups.
Posted in Associative rings and algebras -- Modules, bimodules and ideals -- Modules, bimodules and ideals

Groups, Rings, and Group Rings

International Conference : Groups, Rings, and Group Rings, July 28-August 2, 2008, Ubatuba, Brazil

Author: A. Giambruno,César Polcino Milies,Sudarshan K. Sehgal

Publisher: American Mathematical Soc.

ISBN: 0821847716

Category: Mathematics

Page: 270

View: 3602

This volume represents the proceedings of the conference on Groups, Rings and Group Rings, held July 28 - August 2, 2008, in Ubatuba, Brazil. Papers in this volume contain results in active research areas in the theory of groups, group rings and algebras (including noncommutative rings), polynomial identities, Lie algebras and superalgebras. In particular, topics such as growth functions on varieties, groups of units in group rings, representation theory of Lie algebras, Jordan, alternative and Leibniz algebras, graded identities, automorphisms of trees, and partial actions, are discussed.
Posted in Mathematics

Groups, Rings And Modules With Applications

Author: M.R. Adhikari,A. Adhikari

Publisher: Universities Press

ISBN: 9788173714290

Category: Commutative rings

Page: 310

View: 3459

Posted in Commutative rings

A Guide to Groups, Rings, and Fields

Author: Fernando Q. Gouvêa

Publisher: MAA

ISBN: 0883853558

Category: Mathematics

Page: 309

View: 2963

This Guide offers a concise overview of the theory of groups, rings, and fields at the graduate level, emphasizing those aspects that are useful in other parts of mathematics. It focuses on the main ideas and how they hang together. It will be useful to both students and professionals. In addition to the standard material on groups, rings, modules, fields, and Galois theory, the book includes discussions of other important topics that are often omitted in the standard graduate course, including linear groups, group representations, the structure of Artinian rings, projective, injective and flat modules, Dedekind domains, and central simple algebras. All of the important theorems are discussed, without proofs but often with a discussion of the intuitive ideas behind those proofs. Those looking for a way to review and refresh their basic algebra will benefit from reading this Guide, and it will also serve as a ready reference for mathematicians who make use of algebra in their work.
Posted in Mathematics

Groups, Rings and Fields

Author: David A.R. Wallace

Publisher: Springer Science & Business Media

ISBN: 1447104250

Category: Mathematics

Page: 248

View: 8397

This is a basic introduction to modern algebra, providing a solid understanding of the axiomatic treatment of groups and then rings, aiming to promote a feeling for the evolutionary and historical development of the subject. It includes problems and fully worked solutions, enabling readers to master the subject rather than simply observing it.
Posted in Mathematics

Representation Theory, Group Rings, and Coding Theory

Papers in Honor of S.D. Berman (1922-1987)

Author: M. Isaacs

Publisher: American Mathematical Soc.

ISBN: 0821850989

Category: Mathematics

Page: 357

View: 6593

This volume is dedicated to the memory of the Soviet mathematician S. D. Berman (1922-1987). Berman's work - for the most part in representation theory, group rings, and coding theory - is discussed here in a number of review articles. Among the topics covered are Berman's achievements in coding theory, including his pioneering work on abelian codes and his results on the theory of threshold functions. Also discussed are his contributions to the representation theory of groups over fields, his work on integral representations of groups, his accomplishments in infinite abelian group rings, and his fundamental results on units in integral group rings. In addition, there are 22 research articles written by an international group of researchers in areas of Berman's major interest.
Posted in Mathematics

Abstract Algebra

Introduction to Groups, Rings and Fields with Applications Second Edition

Author: Clive Reis,Stuart A Rankin

Publisher: World Scientific Publishing Company

ISBN: 9814730564

Category: Mathematics

Page: 576

View: 6491

This second edition covers essentially the same topics as the first. However, the presentation of the material has been extensively revised and improved. In addition, there are two new chapters, one dealing with the fundamental theorem of finitely generated abelian groups and the other a brief introduction to semigroup theory and automata. This book is appropriate for second to fourth year undergraduates. In addition to the material traditionally taught at this level, the book contains several applications: Polya–Burnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes, and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3-space, semigroups and automata. It is hoped that these applications will help the reader achieve a better grasp of the rather abstract ideas presented and convince him/her that pure mathematics, in addition to having an austere beauty of its own, can be applied to solving practical problems. Considerable emphasis is placed on the algebraic system consisting of the congruence classes mod n under the usual operations of addition and multiplication. The reader is thus introduced — via congruence classes — to the idea of cosets and factor groups. This enables the transition to cosets and factor objects to be relatively painless. In this book, cosets, factor objects and homomorphisms are introduced early on so that the reader has at his/her disposal the tools required to give elegant proofs of the fundamental theorems. Moreover, homomorphisms play such a prominent role in algebra that they are used in this text wherever possible.
Posted in Mathematics

Groups, Rings and Group Rings

Author: Antonio Giambruno

Publisher: CRC Press

ISBN: 9781138402034

Category:

Page: N.A

View: 4180

This book is a collection of research papers and surveys on algebra that were presented at the Conference on Groups, Rings, and Group Rings held in Ubatuba, Brazil. This text familiarizes researchers with the latest topics, techniques, and methodologies in several branches of contemporary algebra. With extensive coverage, it examines broad themes from group theory and ring theory, exploring their relationship with other branches of algebra including actions of Hopf algebras, groups of units of group rings, combinatorics of Young diagrams, polynomial identities, growth of algebras, and more. Featuring international contributions, this book is ideal for mathematicians specializing in these areas.
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Group Rings and Class Groups

Author: K.W. Roggenkamp,M.J. Taylor

Publisher: Birkhäuser

ISBN: 303488611X

Category: Mathematics

Page: 210

View: 7742

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.
Posted in Mathematics

Groups, Rings and Galois Theory

Second Edition

Author: Victor P Snaith

Publisher: World Scientific Publishing Company

ISBN: 9813102233

Category: Mathematics

Page: 228

View: 2253

This book is ideally suited for a two-term undergraduate algebra course culminating in a discussion on Galois theory. It provides an introduction to group theory and ring theory en route. In addition, there is a chapter on groups — including applications to error-correcting codes and to solving Rubik's cube. The concise style of the book will facilitate student-instructor discussion, as will the selection of exercises with various levels of difficulty. For the second edition, two chapters on modules over principal ideal domains and Dedekind domains have been added, which are suitable for an advanced undergraduate reading course or a first-year graduate course.
Posted in Mathematics

Basic Algebra

Groups, Rings and Fields

Author: P.M. Cohn

Publisher: Springer Science & Business Media

ISBN: 0857294288

Category: Mathematics

Page: 465

View: 8815

This is the first volume of a revised edition of P.M. Cohn's classic three-volume text Algebra, widely regarded as one of the most outstanding introductory algebra textbooks. This volume covers the important results of algebra. Readers should have some knowledge of linear algebra, groups and fields, although all the essential facts and definitions are recalled.
Posted in Mathematics

Algebra

Groups, Rings, and Fields

Author: Louis Rowen

Publisher: A K Peters/CRC Press

ISBN: 9781568810287

Category: Mathematics

Page: 264

View: 1194

This text presents the concepts of higher algebra in a comprehensive and modern way for self-study and as a basis for a high-level undergraduate course. The author is one of the preeminent researchers in this field and brings the reader up to the recent frontiers of research including never-before-published material. From the table of contents: - Groups: Monoids and Groups - Cauchyís Theorem - Normal Subgroups - Classifying Groups - Finite Abelian Groups - Generators and Relations - When Is a Group a Group? (Cayley's Theorem) - Sylow Subgroups - Solvable Groups - Rings and Polynomials: An Introduction to Rings - The Structure Theory of Rings - The Field of Fractions - Polynomials and Euclidean Domains - Principal Ideal Domains - Famous Results from Number Theory - I Fields: Field Extensions - Finite Fields - The Galois Correspondence - Applications of the Galois Correspondence - Solving Equations by Radicals - Transcendental Numbers: e and p - Skew Field Theory - Each chapter includes a set of exercises
Posted in Mathematics

Algebra in Action: A Course in Groups, Rings, and Fields

Author: Shahriar Shahriar

Publisher: American Mathematical Soc.

ISBN: 1470428490

Category: Algebra

Page: 675

View: 9674

This text—based on the author's popular courses at Pomona College—provides a readable, student-friendly, and somewhat sophisticated introduction to abstract algebra. It is aimed at sophomore or junior undergraduates who are seeing the material for the first time. In addition to the usual definitions and theorems, there is ample discussion to help students build intuition and learn how to think about the abstract concepts. The book has over 1300 exercises and mini-projects of varying degrees of difficulty, and, to facilitate active learning and self-study, hints and short answers for many of the problems are provided. There are full solutions to over 100 problems in order to augment the text and to model the writing of solutions. Lattice diagrams are used throughout to visually demonstrate results and proof techniques. The book covers groups, rings, and fields. In group theory, group actions are the unifying theme and are introduced early. Ring theory is motivated by what is needed for solving Diophantine equations, and, in field theory, Galois theory and the solvability of polynomials take center stage. In each area, the text goes deep enough to demonstrate the power of abstract thinking and to convince the reader that the subject is full of unexpected results.
Posted in Algebra

Abelian Groups, Rings, and Modules

AGRAM 2000 Conference July 9-15, 2000, Perth, Western Australia

Author: Australia) Kelarev (University of Tasmania

Publisher: American Mathematical Soc.

ISBN: 0821827510

Category: Mathematics

Page: 308

View: 5677

This volume presents the proceedings from the conference on Abelian Groups, Rings, and Modules (AGRAM) held at the University of Western Australia (Perth). Included are articles based on talks given at the conference, as well as a few specially invited papers. The proceedings are dedicated to Professor Laszlo Fuchs. The book includes a tribute and a review of his work by his long-time collaborator, Professor Luigi Salce. Four surveys from leading experts follow Professor Salce's article.They present recent results from active research areas: error correcting codes as ideals in group rings, duality in module categories, automorphism groups of abelian groups, and generalizations of isomorphism in torsion-free abelian groups. In addition to these surveys, the volume contains 22 research articles in diverse areas connected with the themes of the conference. The areas discussed include abelian groups and their endomorphism rings, modules over various rings, commutative and non-commutative ring theory, varieties of groups, and topological aspects of algebra. The book offers a comprehensive source for recent research in this active area of study.
Posted in Mathematics

An Introduction to Group Rings

Author: César Polcino Milies,Sudarshan K. Sehgal

Publisher: Springer Science & Business Media

ISBN: 9781402002380

Category: Mathematics

Page: 371

View: 2789

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 .
Posted in Mathematics

Groups, Rings and Algebras

A Conference in Honor of Donald S. Passman, June 10-12, 2005, the University of Wisconsin-Madison, Madison, Wisconsin

Author: Donald S. Passman

Publisher: American Mathematical Soc.

ISBN: 0821839047

Category: Mathematics

Page: 301

View: 3412

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.
Posted in Mathematics

Class Groups and Picard Groups of Group Rings and Orders

Author: Irving Reiner

Publisher: American Mathematical Soc.

ISBN: 0821816764

Category: Mathematics

Page: 44

View: 718

The aim of the lectures is to provide an introduction to recent developments in the theory of class groups and Picard groups. The techniques employed come from the three main areas: algebraic number theory, representation theory of algebras and orders, and algebraic $K$-theory.
Posted in Mathematics

Groups, Rings, Modules

Author: Maurice Auslander,David Buchsbaum

Publisher: Courier Corporation

ISBN: 048679542X

Category: Mathematics

Page: 480

View: 832

Classic monograph covers sets and maps, monoids and groups, unique factorization domains, localization and tensor products, applications of fundamental theorem, algebraic field extension, Dedekind domains, and much more. 1974 edition.
Posted in Mathematics

Abelian Groups, Rings, Modules, and Homological Algebra

Author: Pat Goeters,Overtoun M.G. Jenda

Publisher: CRC Press

ISBN: 9781420010763

Category: Mathematics

Page: 360

View: 7476

About the book... In honor of Edgar Enochs and his venerable contributions to a broad range of topics in Algebra, top researchers from around the world gathered at Auburn University to report on their latest work and exchange ideas on some of today's foremost research topics. This carefully edited volume presents the refereed papers of the participants of these talks along with contributions from other veteran researchers who were unable to attend. These papers reflect many of the current topics in Abelian Groups, Commutative Algebra, Commutative Rings, Group Theory, Homological Algebra, Lie Algebras, and Module Theory. Accessible even to beginning mathematicians, many of these articles suggest problems and programs for future study. This volume is an outstanding addition to the literature and a valuable handbook for beginning as well as seasoned researchers in Algebra. about the editors... H. PAT GOETERS completed his undergraduate studies in mathematics and computer science at Southern Connecticut State University and received his Ph.D. in 1984 from the University of Connecticut under the supervision of William J. Wickless. After spending one year in a post-doctoral position in Wesleyan University under the tutelage of James D. Reid, Goeters was invited for a tenure track position in Auburn University by Ulrich F. Albrecht. Soon afterwards, William Ullery and Overtoun Jenda were hired, and so began a lively Algebra group. OVERTOUN M. G. JENDA received his bachelor's degree in Mathematics from Chancellor College, the University of Malawi. He moved to the U.S. 1977 to pursue graduate studies at University of Kentucky, earning his Ph.D. in 1981 under the supervision of Professor Edgar Enochs. He then returned to Chancellor College, where he was a lecturer (assistant professor) for three years. He moved to the University of Botswana for another three-year stint as a lecturer before moving back to the University of Kentucky as a visiting assistant professor in 1987. In 1988, he joined the Algebra research group at Auburn University.
Posted in Mathematics

Free Group Rings

Author: Narain Gupta

Publisher: American Mathematical Soc.

ISBN: 0821850725

Category: Mathematics

Page: 129

View: 2170

Posted in Mathematics