An Introduction To Group Rings

Author : César Polcino Milies,S.K. Sehgal
Publisher : Springer Science & Business Media
Page : 394 pages
File Size : 55,9 Mb
Release : 2002-01-31
Category : Mathematics
ISBN : 1402002386

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An Introduction to Group Rings by César Polcino Milies,S.K. Sehgal Pdf

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 .

Author : Donald S. Passman
Publisher : Courier Corporation
Page : 754 pages
File Size : 41,9 Mb
Release : 2011-01-01
Category : Mathematics
ISBN : 9780486482064

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The Algebraic Structure of Group Rings by Donald S. Passman Pdf

"'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"--

Author : R. B. J. T. Allenby
Publisher : Butterworth-Heinemann
Page : 383 pages
File Size : 45,7 Mb
Release : 1991
Category : Mathematics
ISBN : 0340544406

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Rings, Fields and Groups by R. B. J. T. Allenby Pdf

Provides an introduction to the results, methods and ideas which are now commonly studied in abstract algebra courses

Author : A. Giambruno,César Polcino Milies,Sudarshan K. Sehgal
Publisher : American Mathematical Soc.
Page : 283 pages
File Size : 49,6 Mb
Release : 2009
Category : Group rings
ISBN : 9780821847718

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Groups, Rings and Group Rings by A. Giambruno,César Polcino Milies,Sudarshan K. Sehgal Pdf

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.

Author : César Polcino Milies,S.K. Sehgal
Publisher : Springer
Page : 0 pages
File Size : 42,9 Mb
Release : 2002-03-14
Category : Mathematics
ISBN : 9401004056

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An Introduction to Group Rings by César Polcino Milies,S.K. Sehgal Pdf

Author : Joseph J. Rotman
Publisher : Springer Science & Business Media
Page : 447 pages
File Size : 50,9 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781461245766

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An Introduction to Algebraic Topology by Joseph J. Rotman Pdf

A clear exposition, with exercises, of the basic ideas of algebraic topology. Suitable for a two-semester course at the beginning graduate level, it assumes a knowledge of point set topology and basic algebra. Although categories and functors are introduced early in the text, excessive generality is avoided, and the author explains the geometric or analytic origins of abstract concepts as they are introduced.

Author : David A.R. Wallace
Publisher : Springer Science & Business Media
Page : 256 pages
File Size : 50,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447104254

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Groups, Rings and Fields by David A.R. Wallace Pdf

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.

Author : Shahriar Shahriar
Publisher : American Mathematical Soc.
Page : 675 pages
File Size : 42,9 Mb
Release : 2017-08-16
Category : Algebra
ISBN : 9781470428495

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Algebra in Action: A Course in Groups, Rings, and Fields by Shahriar Shahriar Pdf

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.

Author : Steve Warner
Publisher : Unknown
Page : 346 pages
File Size : 43,5 Mb
Release : 2019-07-28
Category : Mathematics
ISBN : 0999811789

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Abstract Algebra for Beginners by Steve Warner Pdf

"This book [provides] a basic but rigorous introduction to abstract algebra." --

Author : Clive Reis,Stuart A. Rankin
Publisher : World Scientific Publishing Company
Page : 555 pages
File Size : 44,7 Mb
Release : 2016-05-31
Category : Mathematics
ISBN : 9814730548

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Abstract Algebra: an Introduction to Groups, Rings and Fields (2nd Edition) by Clive Reis,Stuart A. Rankin Pdf

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.

Author : A. J. Berrick,M. E. Keating
Publisher : Cambridge University Press
Page : 286 pages
File Size : 55,9 Mb
Release : 2000-05
Category : Mathematics
ISBN : 0521632749

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An Introduction to Rings and Modules by A. J. Berrick,M. E. Keating Pdf

This is a concise 2000 introduction at graduate level to ring theory, module theory and number theory.

Author : Paul M. Cohn
Publisher : Springer Science & Business Media
Page : 234 pages
File Size : 45,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447104759

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Introduction to Ring Theory by Paul M. Cohn Pdf

A clear and structured introduction to the subject. After a chapter on the definition of rings and modules there are brief accounts of Artinian rings, commutative Noetherian rings and ring constructions, such as the direct product, Tensor product and rings of fractions, followed by a description of free rings. Readers are assumed to have a basic understanding of set theory, group theory and vector spaces. Over two hundred carefully selected exercises are included, most with outline solutions.

Author : Louis Rowen
Publisher : CRC Press
Page : 264 pages
File Size : 44,6 Mb
Release : 2018-10-08
Category : Mathematics
ISBN : 9781439863527

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Algebra by Louis Rowen Pdf

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

Author : Benjamin Fine,Anthony M. Gaglione,Gerhard Rosenberger
Publisher : JHU Press
Page : 583 pages
File Size : 51,8 Mb
Release : 2014-07-01
Category : Mathematics
ISBN : 9781421411774

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Introduction to Abstract Algebra by Benjamin Fine,Anthony M. Gaglione,Gerhard Rosenberger Pdf

A new approach to abstract algebra that eases student anxieties by building on fundamentals. Introduction to Abstract Algebra presents a breakthrough approach to teaching one of math's most intimidating concepts. Avoiding the pitfalls common in the standard textbooks, Benjamin Fine, Anthony M. Gaglione, and Gerhard Rosenberger set a pace that allows beginner-level students to follow the progression from familiar topics such as rings, numbers, and groups to more difficult concepts. Classroom tested and revised until students achieved consistent, positive results, this textbook is designed to keep students focused as they learn complex topics. Fine, Gaglione, and Rosenberger's clear explanations prevent students from getting lost as they move deeper and deeper into areas such as abelian groups, fields, and Galois theory. This textbook will help bring about the day when abstract algebra no longer creates intense anxiety but instead challenges students to fully grasp the meaning and power of the approach. Topics covered include: • Rings • Integral domains • The fundamental theorem of arithmetic • Fields • Groups • Lagrange's theorem • Isomorphism theorems for groups • Fundamental theorem of finite abelian groups • The simplicity of An for n5 • Sylow theorems • The Jordan-Hölder theorem • Ring isomorphism theorems • Euclidean domains • Principal ideal domains • The fundamental theorem of algebra • Vector spaces • Algebras • Field extensions: algebraic and transcendental • The fundamental theorem of Galois theory • The insolvability of the quintic

Author : R. B. J. T. Allenby
Publisher : Hodder Education
Page : 422 pages
File Size : 49,5 Mb
Release : 1983
Category : Mathematics
ISBN : UCSC:32106016516962

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Rings, Fields and Groups by R. B. J. T. Allenby Pdf

This book provides a stimulating and unusiual introduction to the results, methods and ideas which are now commonly studied in abstract algebra courses in universities and polytechnics. The mixture of informal and formal presentation generates the enthusiasm of the reader without neglecting the axiomatic approach necessary for the serious study.