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**About this book :- **
**Exercises in Classical Ring Theory ** written by
** T. Y. Lam **

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.

(T. Y. Lam)

**Book Detail :- **
** Title: ** Exercises in Classical Ring Theory
** Edition: **
** Author(s): ** Tsit Yuen Lam
** Publisher: ** Springer
** Series: ** Problem books in mathematics
** Year: ** 2003
** Pages: ** 380
** Type: ** PDF
** Language: ** English
** ISBN: ** 0387005005,9780387005003,9780387217710
** Country: ** US

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**About Author :- **

Author ** Tsit Yuen Lam ** (born 1942) is a Hong Kong-American mathematician specializing in algebra, especially ring theory and quadratic forms.

Lam earned his bachelor's degree at the University of Hong Kong in 1963 and his Ph.D. at Columbia University in 1967 under Hyman Bass, with a thesis titled On Grothendieck Groups.

He start his career as an instructor at the University of Chicago after complete his eductaion. He became assistant professor in 1969, associate professor in 1972, and full professor in 1976. He served as assistant department head several times. From 1995 to 1997 he was Deputy Director of the Mathematical Sciences Research Institute in Berkeley, California. He was awarded the Leroy P. Steele Prize for his textbooks in 1982. He became a fellow of the American Mathematical Society in 2012.

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** • Download PDF A First Course in Rings and Ideals by David M. Burton **

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**Book Contents :- **
**Exercises in Classical Ring Theory ** written by
** T. Y. Lam **
cover the following topics.

Preface to the Second Edition

Preface to the First Edition

Notes to the Reader .

1. Wedderburn-Artin Theory

2. Jacobson Radical Theory

3. Introduction to Representation Theory

4. Prime and Primitive Rings

5. Introduction to Division Rings

6. Ordered Structures in Rings

7. Local Rings, Semilocal Rings, and Idempotents

8. Perfect and Semiperfect Rings

Name Index

Subject Index

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