環(huán)和模的范疇第2版

內(nèi)容概要

本書是一部研究生教材。作者采用范疇理論而不是算術(shù)方式論述環(huán)與模的基本理論，內(nèi)容從環(huán)、模、同態(tài)、直接和、擬合條件等基本知識一直延伸到Wedderburn-Artin定理、Jacobson根基、張量函數(shù)、Morita等價和對偶、內(nèi)射模和射影模的分解論、半完備環(huán)和完環(huán)，以及同類書很少論及的同調(diào)論、商環(huán)和交換環(huán)等課題，本版新增內(nèi)容為阿廷環(huán)的經(jīng)典結(jié)果。

作者簡介

GTM13

書籍目錄

Preface   O. Preliminaries Chapter 1: Rinos， Modules and Homomorphisms   1. Review of Rings and their Homomorphisms   2. Modules and Submodules   3. Homomorphisms of Modules   4. Categories of Modules； Endomorphism Rings Chapter 2: Direct Sums and Products   5. Direct Summands   6. Direct Sums and Products of Modules   7. Decomposition of Rings   8. Generating and Cogenerating Chapter 3: Finiteness Conditions for Modules   9. Semisimple Modules--The Socle and the Radical   10. Finitely Generated and Finitely Cogenerated Modules-Chain Conditions   11. Modules with Composition Series   12. Indecomposable Decompositions of Modules Chapter 4: Classical Ring-Structure Theorems   13. Semisimple Rings   14. The Density Theorem   15. The Radical of a Ring-Local Rings and Artinian RingsChapter 5: Functors Between Module Categories  16.The Hom Functors and Exactness-Projectivity and Injectivity  17.Projective Modules and Generators  18.Injective Modules and Cogenerators  19.The Tensor Functors and Flat Modules  20.Natural TransformationsChapter 6: Equivalence and Duality for Module Categories  21.Equivalent Rings  22.The Morita Characterizations of Equivalence  23.Dualities  24.Morita DualitiesChapter 7: Injective Modules,Projective Modules,and Their Decompositions  25.Injective Modules and Noetherian Rings-The Faith-Walker Theorems  26.Direct Sums of Countably Generated Modules-With Local Endomorphism Rings  27.Semiperfect Rings  28.Perfect Rings  29.Modules with Perfect Endomorphism RingsChapter 8: Classical Artinian Rings  30.Artinian Rings with Duality  31.Injective Projective Modules  32.Serial RingsBibliographyIndex

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