A First Course in Noncommutative Rings

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Springer Science & Business Media, Jan 6, 2013 - Mathematics - 388 pages
This book, 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 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.
 

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Contents

2 Semisimplicity
48
3 Structure of Semisimple Rings
116
8 Representations of Groups
117
9 Linear Groups
141
CHAPTER 2
147
Jacobson Radical Theory OIIOCM J OOOOIIUJO
154
12 Subdirect Products and Commutativity Theorems
191
5 Jacobson Radical Under Change of Rings
214
CHAPTER 6
261
6 Group Rings and the JSemisimplicity Problem
276
CHAPTER 7
279
20 Semilocal Rings
296
7 Modules over FiniteDimensional Algebras
306
22 Central Idempotents and Block Decompositions
326
Perfect and Semiperfect Rings
335
25 Principal Indecomposables and Basic Rings
359

l4 Some Classical Constructions
216
15 Tensor Products and Maximal Subfields
238
Name Index
373
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