Preface |
Rings and Modules / Chapter I: |
Preliminaries / 1: |
Projective modules / 2: |
Injective modules / 3: |
Semi-simple rings / 4: |
Hereditary rings / 5: |
Semi-hereditary rings / 6: |
Noetherian rings / 7: |
Exercises |
Additive Functors / Chapter II: |
Definitions |
Examples |
Operators |
Preservation of exactness |
Composite functors |
Change of rings |
Satellites / Chapter III: |
Definition of satellites |
Connecting homomorphisms |
Half exact functors |
Connected sequence of functors |
Axiomatic description of satellites |
Several variables |
Homology / Chapter IV: |
Modules with differentiation |
The ring of dual numbers |
Graded modules, complexes |
Double gradings and complexes |
Functors of complexes |
The homomorphism x |
The homomorphism x (continuation) |
Kunneth relations / 8: |
Derived Functors / Chapter V: |
Complexes over modules; resolutions |
Resolutions of sequences |
Definition of derived functors |
The functors ROT and LOT |
Comparison with satellites |
Computational devices |
Partial derived functors |
Sums, products, limits / 9: |
The sequence of a map / 10: |
Derived Functors of 0 and Hom / Chapter VI: |
The functors Tor and Ext |
Dimension of modules and rings |
Duality homomorphisms |
Integral Domains / Chapter VII: |
Generalities |
The field of quotients |
Inversible ideals |
Prufer rings |
Dedekind rings |
Abelian groups |
A description of Tor1, (A,C) |
Augmented Rings / Chapter VIII: |
Homology and cohomology of an augmented ring |
Dimension |
Faithful systems |
Applications to graded and local rings |
Associative Algebras / Chapter IX: |
Algebras and their tensor products |
Associativity formulae |
The enveloping algebra Ae |
Homology and cohomology of algebras |
The Hochschild groups as functors of A |
Standard complexes |
Supplemented Algebras / Chapter X: |
Homology of supplemented algebras |
Comparison with Hochschild groups |
Augmented monoids |
Groups |
Examples of resolutions |
The inverse process |
Subalgebras and subgroups |
Weakly injective and projective modules |
Products / Chapter XI: |
External products |
Formal properties of the products |
Isomorphisms |
Internal products |
Computation of products |
Products in the Hochschild theory |
Products for supplemented algebras |
Reduction theorems 225 Exercises |
Finite Groups / Chapter XII: |
Norms |
The complete derived sequence |
Complete resolutions |
Products for finite groups |
The uniqueness theorem |
Duality |
Relations with subgroups |
Double cosets |
p-groups and Sylow groups |
Periodicity 260 Exercises / 11: |
Lie Algebras / Chapter XIII: |
Lie algebras and their enveloping algebras |
Homology and cohomology of Lie algebras |
The Poincare-Witt theorem |
Subalgebras and ideals |
The diagonal map and its applications |
A relation in the standard complex |
The complex V(g) |
Applications of the complex V(g) |
Extensions / Chapter XIV: |
Extensions of modules |
Extensions of |
Preface |
Rings and Modules / Chapter I: |
Preliminaries / 1: |
Projective modules / 2: |
Injective modules / 3: |
Semi-simple rings / 4: |