| 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： |
図書
Théorème d'Atiyah-Singer sur l'indice d'un opérateur différentiel elliptique (fasc. 1 ; fasc. 2)