Tsit-Yuen Lam

Lectures on Modules and Rings (eBook, PDF)

• Format: PDF

Produktbeschreibung

This new book can be read independently from the first volume and may be used for lecturing, seminar- and self-study, or for general reference. It focuses more on specific topics in order to introduce readers to a wealth of basic and useful ideas without the hindrance of heavy machinery or undue abstractions. User-friendly with its abundance of examples illustrating the theory at virtually every step, the volume contains a large number of carefully chosen exercises to provide newcomers with practice, while offering a rich additional source of information to experts. A direct approach is used in order to present the material in an efficient and economic way, thereby introducing readers to a considerable amount of interesting ring theory without being dragged through endless preparatory material.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: Springer US
• Seitenzahl: 557
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781461205258
• Artikelnr.: 44052211

Inhaltsangabe

1 Free Modules, Projective, and Injective Modules.- 1. Free Modules.- 2. Projective Modules.- 3. Injective Modules.- 31. Matlis' Theory.- 2 Flat Modules and Homological Dimensions.- 4. Flat and Faithfully Flat Modules.- 41. Faithfully Flat Modules.- 5. Homological Dimensions.- 3 More Theory of Modules.- 6. Uniform Dimensions, Complements, and CS Modules.- 7. Singular Submodules and Nonsingular Rings.- 8. Dense Submodules and Rational Hulls.- 4 Rings of Quotients.- 9. Noncommutative Localization.- 10. Classical Rings of Quotients.- 11. Right Goldie Rings and Goldie's Theorems.- 12. Artinian Rings of Quotients.- 5 More Rings of Quotients.- 13. Maximal Rings of Quotients.- 14. Martindale Rings of Quotients.- 6 Frobenius and Quasi-Frobenius Rings.- 15. Quasi-Frobenius Rings.- 16. Frobenius Rings and Symmetric Algebras.- 7 Matrix Rings, Categories of Modules, and Morita Theory.- 17. Matrix Rings.- 18. Morita Theory of Category Equivalences.- 19. Morita Duality Theory.- References.- Name Index.

Rezensionen

"As in the previous book, the presentation is extremely clear and incisive and the exercises are both interesting and challenging. Without a doubt, the book could indeed serve as a textbook for a very good---though definitely formidable---graduate course in ring theory. The author is the first to admit, in his introduction, that he is far from having covered all of the interesting topics in noncommutative ring theory. Therefore, given the high level of presentation of the two books he has already published, one can only hope that a third volume will be in the offing, despite his "solemn pledge" to the contrary."--MATHEMATICAL REVIEWS