Table of Contents

§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 Sode 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: Functors Between Module Categories.- §16. The Horn 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.- 8: Classical Artinian Rings.- §30. Artinian Rings with Duality.- §31. Injective Projective Modules.- §32. Serial Rings.- References.