Lectures on Modules and Rings

Inbunden, Engelska, 1998

Av Tsit-Yuen Lam

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This is the long awaited sequel to Lam's earlier GTM 131 "A First Course in Noncommutative Ring Theory" which received the following praise in the Monthly: "The book is beautifully written with many illuminating examples and exercises ...Reading Lam's book reminded me of my own delight in discovering the structure theory of rings and its applications ...I eagerly await Lam's second volume and confidently recommend his first." -Lance Small This new book can be read independently from the first volume and is intended to be used for lecturing, seminar- and self-study, and for general reference. It is focused more on specific topics in order to introduce the reader to a wealth of basic and useful ideas without the hindrance of heavy machinery or undue abstractions. This volume is particularly user-friendly with its abundance of examples illustrating the theory virtually at every step. A large number of carefully chosen exercises serves the dual purpose of providing practice to newcomers to the field, and 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 the reader to a considerable amount of interesting ring theory without being dragged through endless preparatory material.

Produktinformation

Utgivningsdatum1998-10-23
Mått160 x 240 x 35 mm
Vikt950 g
FormatInbunden
SpråkEngelska
SerieGraduate Texts in Mathematics
Antal sidor557
Upplaga1999
FörlagSpringer-Verlag New York Inc.
ISBN9780387984285

Tillhör följande kategorier

Algebra inom Naturvetenskap och teknik

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.

"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