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1.

図書

図書
H. Cartan et C. Chevalley
出版情報: Paris : Secrétariat mathématique, 1956  1 v. (various pagings) ; 28 cm
シリーズ名: Séminaire Henri Cartan ; 8e année, 1955/1956
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2.

図書

図書
Henri Cartan
出版情報: Paris : Secrétariat mathématique, 1956  1 v. (various pagings) ; 27 cm
シリーズ名: Séminaire Henri Cartan ; 2e année, 1949/1950
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3.

図書

図書
Henri Cartan
出版情報: Paris : Secrétariat mathématique, 1956  1 v. (various pagings) ; 27 cm
シリーズ名: Séminaire Henri Cartan ; 7e année, 1954/1955
所蔵情報: loading…
4.

図書

図書
by Henri Cartan and Samuel Eilenberg
出版情報: Princeton : Princeton University Press, 1956  xv, 390 p. ; 24 cm
シリーズ名: Princeton mathematical series ; 19
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目次情報: 続きを見る
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:
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