非交换环初级教程 第2版 英文PDF电子书下载

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