Author | Anderson, Frank W. author |
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Title | Rings and Categories of Modules [electronic resource] / by Frank W. Anderson, Kent R. Fuller |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1974 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-9913-1 |
Descript | IX, 339 p. online resource |
ยง0. Preliminaries -- 1: Rings, Modules and Homomorphisms -- ยง1. Review of Rings and Their Homomorphisms -- ยง2. Modules and Submodules -- ยง3. Homomorphisms of Modules -- ยง4. Categories of Modules; Endomorphism Rings -- 2: Direct Sums and Products -- ยง5. Direct Summands -- ยง6. Direct Sums and Products of Modules -- ยง7. Decomposition of Rings -- ยง8. Generating and Cogenerating -- 3: Finiteness Conditions for Modules -- ยง9. Semisimple ModulesโThe Socle and the Radical -- ยง10. Finitely Generated and Finitely Cogenerated Modulesโ Chain Conditions -- ยง11. Modules With Composition Series -- ยง12. Indecomposable Decompositions of Modules -- 4: Classical Ring-Structure Theorems -- ยง13. Semisimple Rings -- ยง14. The Density Theorem -- ยง15. The Radical of a RingโLocal Rings and Artinian Rings -- 5: Functions Between Module Categories -- ยง16. The Hom Functors and Exactness โ Projectivity and Injectivity -- ยง17. Projective Modules and Generators -- ยง18. Injective Modules and Cogenerators -- ยง19. The Tensor Functors and Flat Modules -- ยง20. Natural Transformations -- 6: Equivalence and Duality for Module Categories -- ยง21. Equivalent Rings -- ยง22. The Morita Characterizations of Equivalence -- ยง23. Dualities -- ยง24. Morita Dualities -- 7: Injective Modules, Projective Modules and Their Decompositions -- ยง25. Injective Modules and Noetherian Rings-The Faith-Walker Theorems -- ยง26. Direct Sums of Countably Generated Modules-With Local Endomorphism Rings -- ยง27. Semiperfect Rings -- ยง28. Perfect Rings -- ยง29. Modules With Perfect Endomorphism Rings