A First Course in Noncommutative Rings

✍ Scribed by T. Y. Lam (auth.)

• Publisher: Springer-Verlag New York
• Year: 2001
• Tongue: English
• Leaves: 405
• Series: Graduate Texts in Mathematics 131
• Edition: 2
• Category: Library

✦ Synopsis

A First Course in Noncommutative Rings, an outgrowth of the author's lectures at the University of California at Berkeley, is intended as a textbook for a one-semester course in basic 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, local and semilocal rings, perfect and semiperfect rings, etc. By aiming the level of writing at the novice rather than the connoisseur and by stressing th the role of examples and motivation, the author has produced a text that is suitable not only for use in a graduate course, but also for self- study in the subject by interested graduate students. More than 400 exercises testing the understanding of the general theory in the text are included in this new edition.

✦ Table of Contents

Front Matter....Pages i-xix
Wedderburn-Artin Theory....Pages 1-47
Jacobson Radical Theory....Pages 48-100
Introduction to Representation Theory....Pages 101-152
Prime and Primitive Rings....Pages 153-201
Introduction to Division Rings....Pages 202-260
Ordered Structures in Rings....Pages 261-278
Local Rings, Semilocal Rings, and Idempotents....Pages 279-334
Perfect and Semiperfect Rings....Pages 335-369
Back Matter....Pages 370-388

✦ Subjects

Algebra