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Exercises in Modules and Rings

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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.

Author(s): T.Y. Lam
Series: Problem Books in Mathematics
Edition: 1
Publisher: Springer
Year: 2006

Language: English
Pages: 433
City: Berlin

Cover......Page 1
Preface......Page 9
Contents......Page 11
Notes to the Reader......Page 13
Partial List of Notations......Page 15
Partial List of Abbreviations......Page 19
$l. Free Modules......Page 21
$2. Projective Modules......Page 41
$3. Injective Modules......Page 80
$4. Flat Modules......Page 117
$5. Homological Dimensions......Page 151
$6. Uniform Dimensions, Complements, & CS Modules......Page 175
$7. Singular Submodules & Nonsingular Rings......Page 205
$8. Dense Submodules & Rational Hulls......Page 225
$9. Noncommutative Localization......Page 237
$10. Classical Ring of Quotients......Page 242
$11. Right Goldie Rings & Goldie's Theorem......Page 262
$12. Artinian Rings of Quotients......Page 280
$13. Maximal Rings of Quotients......Page 291
$14. Martindal's Ring of Quotients......Page 307
$15. Quasi-Frobenius Rings......Page 319
$16. Frobenius Rings & Symmetric Algebras......Page 335
$17. Matrix Rings......Page 363
$18. Morita Theory of Category Equivalences......Page 373
$19. Morita Duality Theory......Page 398
Name Index......Page 423
Subject Index......Page 427