Exercises in Classical Ring Theory / Edition 2

Exercises in Classical Ring Theory / Edition 2

by T.Y. Lam
     
 

ISBN-10: 0387005005

ISBN-13: 9780387005003

Pub. Date: 06/04/2008

Publisher: Springer New York

The first work of its kind, this volume offers a compendium of some 480 exercises of varying degrees of difficulty in classical ring theory. The material covered includes the Wedderburn-Artin theory of semisimple rings, Jacobson's theory of the radical, representation theory of groups and algebras, prime and semiprime rings, primitive and semiprimitive rings,

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Overview

The first work of its kind, this volume offers a compendium of some 480 exercises of varying degrees of difficulty in classical ring theory. The material covered includes the Wedderburn-Artin theory of semisimple rings, Jacobson's theory of the radical, representation theory of groups and algebras, prime and semiprime rings, primitive and semiprimitive rings, division rings, ordered rings, local and semilocal rings, the theory of idempotents, and perfect and semiperfect rings. Each section begins with an introduction giving the general background and the theoretical basis for the problems that follow. All exercises are solved in full detail; many are accompanied by pertinent historical and bibliographical information, or a commentary on possible improvements and generalizations. An outgrowth of the author's lecture courses and seminars at the University of California at Berkeley, this book provides an excellent introduction to problem-solving in ring theory. It can be used either as a companion to the author's A First Course in Noncommutative Rings (from which most of the exercises are selected), or as a source for independent study. For students and researchers alike, this book will also serve as a handy reference for much of the "folklore" in classical ring theory not usually covered in textbooks. This second edition features more than 80 new exercises, ranging from mildly routine to very challenging. Many of these additional exercises are appearing here for the first time.

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Product Details

ISBN-13:
9780387005003
Publisher:
Springer New York
Publication date:
06/04/2008
Series:
Problem Books in Mathematics Series
Edition description:
2nd ed. 2003
Pages:
364
Product dimensions:
6.10(w) x 9.25(h) x 0.03(d)

Related Subjects

Table of Contents

Preface to the Second Edition
Preface to the First Edition
Notes to the Reader
1Wedderburn-Artin Theory1
2Jacobson Radical Theory49
3Introduction to Representation Theory99
4Prime and Primitive Rings141
5Introduction to Division Rings201
6Ordered Structures in Rings247
7Local Rings, Semilocal Rings, and Idempotents267
8Perfect and Semiperfect Rings325
Name Index349
Subject Index353

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