Ring Theory V2 (eBook)

Front Cover 1
Ring Theory, Volume II 4
Copyright Page 5
Contents 6
Introduction to Volume II 12
Table of Principal Notation for Volume II 14
Chapter 5. Homology and Cohomology 16
5.0 Preliminaries about Diagrams 16
5.1 Resolutions and Projective and Injective Dimension 22
5.2 Homology, Cohomology, and Derived Functors 53
5.3 Separable Algebras and Azumaya Algebras 74
Appendix to Chapter 5 : The Grothendieck Group, and Quillen’s Theorem Revisited 89
Exercises 92
Chapter 6. Rings with Polynomial Identities and Affine Algebras 102
6.1 Rings with Polynomial Identities 103
6.2 Affine Algebras 129
6.3 Affine PI-Algebras 147
6.4 Relatively Free PI-Rings and T-Ideals 177
Exercises 187
Chapter 7. Central Simple Algebras 202
7.1 Structure of Central Simple Algebras 202
7.2 The Brauer Group and the Merkurjev-Suslin Theorem 226
7.3 Special Results 259
Appendix A: The Arithmetic Theory and the Brauer Group 273
Appendix B: The Merkurjev-Suslin Theorem and K-Theory 276
Appendix C: Generics 280
Exercises 283
Chapter 8. Rings from Representation Theory 298
8.1 General Structure Theory of Group algebras 298
8.2 Noetherian Group Rings 325
8.3 Enveloping Algebras 340
8.4 General Ring Theoretic Methods 367
Appendix to Chapter 8: Moody's Theorem 394
Exercises 396
Dimensions for Modules and Rings 412
Major Theorems and Counterexamples for Volume II 414
References 424
Bibliography of Books 424
Collections of Papers 428
Bibliography of Articles 430
Index of References According to Section 462
Cumulative Subject Index for Volumes I and II 466