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Tables of Contents for A First Course in Noncommutative Rings
Chapter/Section Title
Page #
Page Count
Preface to the Second Edition
vii
Preface to the First Edition
ix
Notes to the Reader
xvii
Wedderburn--Artin Theory
1
47
Basic Terminology and Examples
2
23
Exercises for §1
22
3
Semisimplicity
25
5
Exercises for §2
29
1
Structure of Semisimple Rings
30
18
Exercises for §3
45
3
Jacobson Radical Theory
48
53
The Jacobson Radical
50
17
Exercises for §4
63
4
Jacobson Radical Under Change of Rings
67
11
Exercises for §5
77
1
Group Rings and the J-Semisimplicity Problem
78
23
Exercises for §6
98
3
Introduction to Representation Theory
101
52
Modules over Finite-Dimensional Algebras
102
15
Exercises for §7
116
1
Representations of Groups
117
24
Exercises for §8
137
4
Linear Groups
141
12
Exercises for §9
152
1
Prime and Primitive Rings
153
49
The Prime Radical; Prime and Semiprime Rings
154
17
Exercises for §10
168
3
Structure of Primitive Rings; the Density Theorem
171
20
Exercises for §11
188
3
Subdirect Products and Commutativity Theorems
191
11
Exercises for §12
198
4
Introduction to Division Rings
202
59
Division Rings
203
13
Exercises for §13
214
2
Some Classical Constructions
216
22
Exercises for §14
235
3
Tensor Products and Maximal Subfields
238
10
Exercises for §15
247
1
Polynomials over Division Rings
248
13
Exercises for §16
258
3
Ordered Structures in Rings
261
18
Orderings and Preorderings in Rings
262
8
Exercises for §17
269
1
Ordered Division Rings
270
9
Exercises for §18
276
3
Local Rings, Semilocal Rings, and Idempotents
279
56
Local Rings
279
17
Exercises for §19
293
3
Semilocal Rings
296
12
Appendix: Endomorphism Rings of Uniserial Modules
302
4
Exercises for §20
306
2
The Theory of Idempotents
308
18
Exercises for §21
322
4
Central Idempotents and Block Decompositions
326
9
Exercises for §22
333
2
Perfect and Semiperfect Rings
335
35
Perfect and Semiperfect Rings
336
11
Exercises for §23
346
1
Homological Characterizations of Perfect and Semiperfect Rings
347
12
Exercises for §24
358
1
Principal Indecomposables and Basic Rings
359
11
Exercises for §25
368
2
References
370
3
Name Index
373
4
Subject Index
377