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An Introduction to Homological Algebra

by Rotman, Joseph J. A

  • ISBN: 9780125992503
  • ISBN10: 0125992505

An Introduction to Homological Algebra

by Rotman, Joseph J. A

  • Binding: Hardcover
  • Publisher: Academic Press
  • Publish date: 06/01/1979
  • ISBN: 9780125992503
  • ISBN10: 0125992505
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Description: Preface Contents 1. Introduction Line Integrals and Independence of Path Categories and Functors Tensor Products Singular Homology 2. Hom and ? Modules Sums and Products Exactness Adjoints Direct Limits Inverse Limits 3. Projectives, Injectives, and Flats Free Modules Projective Modules Injective Modules Watts' Theorems Flat Modules Purity Localization 4. Specific Rings Noetherian Rings Semisimple Rings Von Neumann Regular Rings Hereditary and Dedekind Rings Semihereditary and Prfer Rings Quasi-Frobenius Rings Local Rings and Artinian Rings Polynomial Rings 5. Extensions of Groups 6. Homology Homology Functors Derived Functors 7. Ext Elementary Properties Ext and Extensions Axioms 8. Tor Elementary Properties Tor and Torsion Universal Coefficient Theorems 9. Son of Specific Rings Dimensions Hilbert's Syzygy Theorem Serre's Theorem Mixed Identities Commutative Noetherian Local Rings 10. The Return of Cohomology of Groups Homology Groups Cohomology Groups Computations and Applications 11. Spectral Sequences Exact Couples and Five-Term Sequences Derived Couples and Spectral Sequences Filtrations and Convergence Bicomplexes Knneth Theorems Grothendieck Spectral Sequences More Groups More Modules References Index
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