Exercises in Modules and Rings

✍ Scribed by T.Y. Lam

• Publisher: Springer
• Year: 2006
• Tongue: English
• Leaves: 432
• Series: Problem Books in Mathematics
• Edition: 1
• Category: Library

✦ Synopsis

This volume offers a compendium of exercises of varying degree of difficulty in the theory of modules and rings. It is the companion volume to GTM 189. All exercises are solved in full detail. Each section begins with an introduction giving the general background and the theoretical basis for the problems that follow.

✦ Table of Contents

Cover......Page 1
Series: Problem Books in Mathematics......Page 2
Exercises in Modules and Rings......Page 4
Copyright......Page 5
Preface......Page 8
Contents......Page 10
Notes to the Reader......Page 12
Partial List of Notations......Page 14
Partial List of Abbreviations......Page 18
§1. Free Modules......Page 20
Exercises for §1......Page 21
§2. Projective Modules......Page 40
Exercises for §2......Page 42
§3. Injective Modules......Page 79
Exercises for §3......Page 80
§4. Flat Modules......Page 116
Exercises for §4......Page 118
§5. Homological Dimensions......Page 150
Exercises for §5......Page 152
§6. Uniform Dimensions, Complements, and CS Modules......Page 174
Exercises for §6......Page 176
§7. Singular Submodules and Nonsingular Rings......Page 204
Exercises for §7......Page 205
§8. Dense Submodules and Rational Hulls......Page 224
Exercises for §8......Page 225
§9. Noncommutative localization......Page 236
Exercises for §9......Page 237
§10. Classical Ring of Quotients......Page 241
Exercises for §10......Page 242
§11. Right Goldie Rings and Goldie's Theorem......Page 261
Exercises for §11......Page 263
§12. Artinian Rings of Quotients......Page 279
Exercises for §12......Page 280
§13. Maximal Rings of Quotients......Page 290
Exercises for §13......Page 292
§14. Martindal's Ring of Quotients......Page 306
Exercises for §14......Page 308
§15. Quasi-Frobenius Rings......Page 318
Exercises for §15......Page 319
§16. Frobenius Rings and Symmetric Algebras......Page 334
Exercises for §16......Page 336
§17. Matrix Rings......Page 362
Exercises for §17......Page 363
§18. Morita Theory of Category Equivalences......Page 372
Exercises for §18......Page 374
§19. Morita Duality Theory......Page 397
Exercises for §19......Page 399
Name Index......Page 422
Subject Index......Page 426