Introduction to Homological Algebra, 85

PrefaceContents1. Introduction Line Integrals and Independence of Path Categories and Functors Tensor Products Singular Homology2. Hom and Ⓧ Modules Sums and Products Exactness Adjoints Direct Limits Inverse Limits3. Projectives, Injectives, and Flats Free Modules Projective Modules Injective Modules Watts’ Theorems Flat Modules Purity Localization4. Specific Rings Noetherian Rings Semisimple Rings Von Neumann Regular Rings Hereditary and Dedekind Rings Semihereditary and Prüfer Rings Quasi-Frobenius Rings Local Rings and Artinian Rings Polynomial Rings5. Extensions of Groups6. Homology Homology Functors Derived Functors7. Ext Elementary Properties Ext and Extensions Axioms8. Tor Elementary Properties Tor and Torsion Universal Coefficient Theorems9. Son of Specific Rings Dimensions Hilbert's Syzygy Theorem Serre's Theorem Mixed Identities Commutative Noetherian Local Rings10. The Return of Cohomology of Groups Homology Groups Cohomology Groups Computations and Applications11. Spectral Sequences Exact Couples and Five-Term Sequences Derived Couples and Spectral Sequences Filtrations and Convergence Bicomplexes Künneth Theorems Grothendieck Spectral Sequences More Groups More ModulesReferencesIndex