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