Exercises in Classical Ring Theory

by Lam, T. Y.

• ISBN13: 9780387005003
• ISBN10: 0387005005
• Edition: 2nd
• Format: Hardcover
• Copyright: 2003-09-01
• Publisher: Springer Nature

Summary

This useful book, which grew out of the author's lectures at Berkeley, presents some 400 exercises of varying degrees of difficulty in classical ring theory, together with complete solutions, background information, historical commentary, bibliographic details, and indications of possible improvements or generalizations. The book should be especially helpful to graduate students as a model of the problem-solving process and an illustration of the applications of different theorems in ring theory. The author also discusses "the folklore of the subject: the 'tricks of the trade' in ring theory, which are well known to the experts in the field but may not be familiar to others, and for which there is usually no good reference". The problems are from the following areas: the Wedderburn-Artin theory of semisimple rings, the Jacobson radical, representation theory of groups and algebras, (semi)prime rings, (semi)primitive rings, division rings, ordered rings, (semi)local rings, the theory of idempotents, and (semi)perfect rings. Problems in the areas of module theory, category theory, and rings of quotients are not included, since they will appear in a later book. T. W. Hungerford, Mathematical Reviews

Table of Contents

Preface

Notes to the Reader

Wedderburn-Artin Theory

Jacobson Radical Theory

Introduction to Representation Theory

Prime and Primitive Rings

Introduction to Division Rings

Ordered Structures in Rings

Local Rings, Semilocal Rings, and Idempotents, Perfect and Semiperfect Rings

Name Index

Subject Index

Table of Contents provided by Publisher. All Rights Reserved.