Lectures on modules and rings / T. Y. Lam

Auteur principal : Lam, Tsit- Yuen, 1942-, AuteurType de document : MonographieCollection : Graduate texts in mathematics, 189Langue : anglais.Pays: Etats Unis.Éditeur : New York : Springer, 1999Description : 1 vol. (XXI-557 p.) : ill. ; 25 cmISBN: 0387984283.ISSN: 0072-5285.Bibliographie : Bibliogr. p. [543]-548. Index .Sujet MSC : 16D10, Modules, bimodules and ideals in associative algebras, General module theory
16E10, Homological methods in associative algebras, Homological dimension
16U20, Associative rings and algebras - Conditions on elements, Ore rings, multiplicative sets, Ore localization
16D40, Modules, bimodules and ideals in associative algebras, Free, projective, and flat modules and ideals
16D50, Modules, bimodules and ideals in associative algebras, Injective modules, self-injective associative ringsEn-ligne : Springerlink | Zentralblatt | MathSciNet
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Contents. Preface. Notes to the reader. Partial list of notations. Partial list of abbreviations. Chapter 1: Free modules, projective, and injective modules (1. Free modules, 2. Projective modules, 3. Injective modules). Chapter 2: Flat modules and homological dimensions (4. Flat and faithfully flat modules, 5. Homological dimensions). Chapter 3: More theory of modules (6. Uniform dimensions, complements, and CS modules, 7. Singular submodules and nonsingular rings, 8. Dense submodules and rational hulls). Chapter 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). Chapter 5: More rings of quotients (13. Maximal rings of quotients, 14. Martindale rings of quotients). Chapter 6: Frobenius and quasi-Frobenius rings (15. Quasi-Frobenius rings, 16. Frobenius rings and symmetric algebras). Chapter 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. Subject index

Bibliogr. p. [543]-548. Index

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