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 Rings Chapter 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 Transformations Chapter 6: Equivalence and Duality for Module Categories 21.Equivalent Rings 22.The Morita Characterizations of Equivalence 23.Dualities 24.Morita Dualities Chapter 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 Rings Chapter 8: Classical Artinian Rings 30.Artinian Rings with Duality 31.Injective Projective Modules 32.Serial Rings Bibliography Index
