CHAPTER 1 Wedderburn-Artin Theory 1
1．Basic Terminology and Examples 2
Exercises for §1 22
2．Semisimplicity 25
Exercises for §2 29
3．Structure of Semisimple Rings 30
Exercises for §3 45
CHAPTER 2 Jacobson Radical Theory 48
4．The Jacobson Radical 50
Exercises for §4 63
5．Jacobson Radical Under Change of Rings 67
Exercises for §5 77
6．Group Rings and the J-Semisimplicity Problem 78
Exercises for §6 98
CHAPTER 3 Introduction to Representation Theory 101
7．Modules over Finite-Dimensional Algebras 102
Exercises for §7 116
8．Representations of Groups 117
Exercises for §8 137
9．Linear Groups 141
Exercises for §9 152
CHAPTER 4 Prime and Primitive Rings 153
10．The Prime Radical;Prime and Semiprime Rings 154
Exercises for §10 168
11．Structure of Primitive Rings;the Density Theorem 171
Exercises for §11 188
12．Subdirect Products and Commutativity Theorems 191
Exercises for §12 198
CHAPTER 5 Introduction to Division Rings 202
13．Division Rings 203
Exercises for §13 214
14．Some Classical Constructions 216
Exercises for §14 235
15．Tensor Products and Maximal Subfields 238
Exercises for §15 247
16．Polynomials over Division Rings 248
Exercises for §16 258
CHAPTER 6 Ordered Structures in Rings 261
17．Orderings and Preorderings in Rings 262
Exercises for §17 269
18．Ordered Division Rings 270
Exercises for §18 276
CHAPTER 7 Local Rings,Semilocal Rings,and Idempotents 279
19．Local Rings 279
Exercises for §19 293
20．Semilocal Rings 296
Appendix:Endomorphism Rings of Uniserial Modules 302
Exercises for §20 306
21．Th Theory of Idempotents 308
Exercises for §21 322
22．Central Idempotents and Block Decompositions 326
Exercises for §22 333
CHAPTER 8 Perfect and Semiperfect Rings 335
23．Perfect and Semiperfect Rings 336
Exercises for §23 346
24．Homological Characterizations of Perfect and Semiperfect Rings 347
Exercises for §24 358
25．Principal Indecomposables and Basic Rings 359
Exercises for §25 368
References 370
Name Index 373
Subject Index 377