Rings and Categories of Modules

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 ModulesThe Sode and the Radical. - 10. Finitely Generated and Finitely Cogenerated ModulesChain 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 RingLocal Rings and Artinian Rings. - 5: Functors Between Module Categories. - 16. The Horn Functors and ExactnessProjectivity 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 RingsThe Faith-Walker Theorems. - 26. Direct Sums of Countably Generated ModulesWith 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. Language: English