Hjem

I. Modules, Diagrams, and Functors.-
1. The Arrow Notation.-
2. Modules.-
3. Diagrams.-
4. Direct Sums.-
5. Free and Projective Modules.-
6. The Functor Horn.-
7. Categories.-
8. Functors.- II. Homology of Complexes.-
1. Differential Groups.-
2. Complexes.-
3. Cohomology.-
4. The Exact Homology Sequence.-
5. Some Diagram Lemmas.-
6. Additive Relations.-
7. Singular Homology.-
8. Homotopy.-
9. Axioms for Homology.- III. Extensions and Resolutions.-
1. Extensions of Modules.-
2. Addition of Extensions.-
3. Obstructions to the Extension of Homomorphisms.-
4. The Universal Coefficient Theorem for Cohomology.-
5. Composition of Extensions.-
6. Resolutions.-
7. Injective Modules.-
8. Injective Resolutions.-
9. Two Exact Sequences for Extn.-
10. Axiomatic Description of Ext.-
11. The Injective Envelope.- IV. Cohomology of Groups.-
1. The Group Ring.-
2. Crossed Homomorphisms.-
3. Group Extensions.-
4. Factor Sets.-
5. The Bar Resolution.-
6. The Characteristic Class of a Group Extension.-
7. Cohomology of Cyclic and Free Groups.-
8. Obstructions to Extensions.-
9. Realization of Obstructions.-
10. SCHUR'S Theorem.-
11. Spaces with Operators.- V. Tensor and Torsion Products.-
1. Tensor Products.-
2. Modules over Commutative Rings.-
3. Bimodules.-
4. Dual Modules.-
5. Right Exactness of Tensor Products.-
6. Torsion Products of Groups.-
7. Torsion Products of Modules.-
8. Torsion Products by Resolutions.-
9. The Tensor Product of Complexes.-
10. The KÜNNETH Formula.-
11. Universal Coefficient Theorems.- VI. Types of Algebras.-
1. Algebras by Diagrams.-
2. Graded Modules.-
3. Graded Algebras.-
4. Tensor Products of Algebras.-
5. Modules over Algebras.-
6. Cohomology of free Abelian Groups.-
7. Differential Graded Algebras.-
8. Identities on Horn and '.-
9. Coalgebras and HOPF Algebras.- VII. Dimension.-
1. Homological Dimension.-
2. Dimensions in Polynomial Rings.-
3. Ext and Tor for Algebras.-
4. Global Dimensions of Polynomial Rings.-
5. Separable Algebras.-
6. Graded Syzygies.-
7. Local Rings.- VIII. Products.-
1. Homology Products.-
2. The Torsion Product of Algebras.-
3. A Diagram Lemma.-
4. External Products for Ext.-
5. Simplicial Objects.-
6. Normalization.-
7. Acyclic Models.-
8. The EILENBERG-ZILBER Theorem.-
9. Cup Products.- IX. Relative Homological Algebra.-
1. Additive Categories.-
2. Abelian Categories.-
3. Categories of Diagrams.-
4. Comparison of Allowable Resolutions.-
5. Relative Abelian Categories.-
6. Relative Resolutions.-
7. The Categorical Bar Resolution.-
8. Relative Torsion Products.-
9. Direct Products of Rings.- X. Cohomology of Algebraic Systems.-
1. Introduction.-
2. The Bar Resolution for Algebras.-
3. The Cohomology of an Algebra.-
4. The Homology of an Algebra.-
5. Homology of Groups and Monoids.-
6. Ground Ring Extensions and Direct Products.-
7. Homology of Tensor Products.-
8. The Case of Graded Algebras.-
9. Complexes of Complexes.-
10. Resolutions and Constructions.-
11. Two-stage Cohomology of DGA-Algebras.-
12. Cohomology of Commutative DGA-Algebras.-
13. Homology of Algebraic Systems.- XI. Spectral Sequences.-
1. Spectral Sequences.-
2. Fiber Spaces.-
3. Filtered Modules.-
4. Transgression.-
5. Exact Couples.-
6. Bicomplexes.-
7. The Spectral Sequence of a Covering.-
8. Cohomology Spectral Sequences.-
9. Restriction, Inflation, and Connection.-
10. The Lyndon Spectral Sequence.-
11. The Comparison Theorem.- XII. Derived Functors.-
1. Squares.-
2. Subobjects and Quotient Objects.-
3. Diagram Chasing.-
4. Proper Exact Sequences.-
5. Ext without Projectives.-
6. The Category of Short Exact Sequences.-
7. Connected Pairs of Additive Functors.-
8. Connected Sequences of Functors.-
9. Derived Functors.-
10. Products by Universality.-
11. Proper Projective Complexes.-
12. The Spectral KÜNNETH Formula.- List of Standard Symbols.