Synopsis
§0. Preliminaries.- 1: Rings, Modules and Homomorphisms.- §1. Review of Rings and Their Homomorphisms.- §2. Modules and Submodules.- §3. Homomorphisms of Modules.- §4. Categories of Modules; Endomorphism Rings.- 2: Direct Sums and Products.- §5. Direct Summands.- §6. Direct Sums and Products of Modules.- §7. Decomposition of Rings.- §8. Generating and Cogenerating.- 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.- 4: Classical Ring-Structure Theorems.- §13. Semisimple Rings.- §14. The Density Theorem.- §15. The Radical of a Ring-Local Rings and Artinian Rings.- 5: Functions 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.- 6: Equivalence and Duality for Module Categories.- §21. Equivalent Rings.- §22. The Morita Characterizations of Equivalence.- §23. Dualities.- §24. Morita Dualities.- 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.
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