Homological Algebra (PMS-19), Volume 19 /

Homological Algebra (PMS-19), Volume 19 / / Henry Cartan, Samuel Eilenberg.

When this book was written, methods of algebraic topology had caused revolutions in the world of pure algebra. To clarify the advances that had been made, Cartan and Eilenberg tried to unify the fields and to construct the framework of a fully fledged theory. The invasion of algebra had occurred on...

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Superior document:Title is part of eBook package: De Gruyter Princeton Mathematical Series eBook Package
VerfasserIn:
Cartan, Henry,
Eilenberg, Samuel,
MitwirkendeR:
Buchsbaum, David A.,
Place / Publishing House:Princeton, NJ : : Princeton University Press, , [2016]
©1956
Year of Publication:2016
Language:English
Series:Princeton Mathematical Series ; 41
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Physical Description:1 online resource (408 p.)
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ctrlnum (DE-B1597)474357
(OCoLC)948780067
collection bib_alma
record_format marc
spelling Cartan, Henry, author. aut http://id.loc.gov/vocabulary/relators/aut
Homological Algebra (PMS-19), Volume 19 / Henry Cartan, Samuel Eilenberg.
Princeton, NJ : Princeton University Press, [2016]
©1956
1 online resource (408 p.)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
text file PDF rda
Princeton Mathematical Series ; 41
Frontmatter -- Preface -- Contents -- Chapter I. Rings and Modules -- Chapter II. Additive Functors -- Chapter III. Satellites -- Chapter IV. Homology -- Chapter V. Derived Functors -- Chapter VI. Derived Functors of ⊗ and Hom -- Chapter VII. Integral Domains -- Chapter VIII. Augmented Rings -- Chapter IX. Associative Algebras -- Chapter X. Supplemented Algebras -- Chapter XI. Products -- Chapter XII. Finite Groups -- Chapter XIII. Lie Algebras -- Chapter XIV. Extensions -- Chapter XV. Spectral Sequences -- Chapter XVI. Applications of Spectral Sequences -- Chapter XVII. Hyperhomology -- Appendix: Exact Categories -- List o f Symbols -- Index o f Terminology
restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star
When this book was written, methods of algebraic topology had caused revolutions in the world of pure algebra. To clarify the advances that had been made, Cartan and Eilenberg tried to unify the fields and to construct the framework of a fully fledged theory. The invasion of algebra had occurred on three fronts through the construction of cohomology theories for groups, Lie algebras, and associative algebras. This book presents a single homology (and also cohomology) theory that embodies all three; a large number of results is thus established in a general framework. Subsequently, each of the three theories is singled out by a suitable specialization, and its specific properties are studied. The starting point is the notion of a module over a ring. The primary operations are the tensor product of two modules and the groups of all homomorphisms of one module into another. From these, "higher order" derived of operations are obtained, which enjoy all the properties usually attributed to homology theories. This leads in a natural way to the study of "functors" and of their "derived functors." This mathematical masterpiece will appeal to all mathematicians working in algebraic topology.
Issued also in print.
Mode of access: Internet via World Wide Web.
In English.
Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022)
Algebra, Homological.
MATHEMATICS / Algebra / Abstract. bisacsh
Abelian group.
Additive group.
Algebra homomorphism.
Algebraic topology.
Anticommutativity.
Associative algebra.
Associative property.
Axiom.
Betti number.
C0.
Category of modules.
Change of rings.
Cohomology.
Cokernel.
Commutative diagram.
Commutative property.
Commutative ring.
Cyclic group.
Derived functor.
Diagram (category theory).
Differential operator.
Direct limit.
Direct product.
Direct sum of modules.
Direct sum.
Duality (mathematics).
Endomorphism.
Epimorphism.
Equivalence class.
Exact category.
Exact sequence.
Existential quantification.
Explicit formulae (L-function).
Factorization.
Field of fractions.
Finite group.
Finitely generated module.
Free abelian group.
Free monoid.
Functor.
Fundamental group.
G-module.
Galois theory.
Global dimension.
Graded ring.
Group algebra.
Hereditary ring.
Hochschild homology.
Homological algebra.
Homology (mathematics).
Homomorphism.
Homotopy.
Hyperhomology.
I0.
Ideal (ring theory).
Inclusion map.
Induced homomorphism.
Injective function.
Injective module.
Integral domain.
Inverse limit.
Left inverse.
Lie algebra.
Linear differential equation.
Mathematical induction.
Maximal ideal.
Module (mathematics).
Monoidal category.
Natural transformation.
Noetherian ring.
Noetherian.
Permutation.
Polynomial ring.
Pontryagin duality.
Product topology.
Projective module.
Quotient algebra.
Quotient group.
Quotient module.
Right inverse.
Ring (mathematics).
Ring of integers.
Separation axiom.
Set (mathematics).
Special case.
Spectral sequence.
Subalgebra.
Subcategory.
Subgroup.
Subring.
Summation.
Tensor product.
Theorem.
Topological space.
Topology.
Trivial representation.
Unification (computer science).
Universal coefficient theorem.
Variable (mathematics).
Zero object (algebra).
Buchsbaum, David A., contributor. ctb https://id.loc.gov/vocabulary/relators/ctb
Eilenberg, Samuel, author. aut http://id.loc.gov/vocabulary/relators/aut
Title is part of eBook package: De Gruyter Princeton Mathematical Series eBook Package 9783110501063 ZDB-23-PMS
Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 9783110442496
print 9780691049915
https://doi.org/10.1515/9781400883844
https://www.degruyter.com/isbn/9781400883844
Cover https://www.degruyter.com/document/cover/isbn/9781400883844/original
language English
format eBook
author Cartan, Henry,
Cartan, Henry,
Eilenberg, Samuel,
spellingShingle Cartan, Henry,
Cartan, Henry,
Eilenberg, Samuel,
Homological Algebra (PMS-19), Volume 19 /
Princeton Mathematical Series ;
Frontmatter --
Preface --
Contents --
Chapter I. Rings and Modules --
Chapter II. Additive Functors --
Chapter III. Satellites --
Chapter IV. Homology --
Chapter V. Derived Functors --
Chapter VI. Derived Functors of ⊗ and Hom --
Chapter VII. Integral Domains --
Chapter VIII. Augmented Rings --
Chapter IX. Associative Algebras --
Chapter X. Supplemented Algebras --
Chapter XI. Products --
Chapter XII. Finite Groups --
Chapter XIII. Lie Algebras --
Chapter XIV. Extensions --
Chapter XV. Spectral Sequences --
Chapter XVI. Applications of Spectral Sequences --
Chapter XVII. Hyperhomology --
Appendix: Exact Categories --
List o f Symbols --
Index o f Terminology
author_facet Cartan, Henry,
Cartan, Henry,
Eilenberg, Samuel,
Buchsbaum, David A.,
Buchsbaum, David A.,
Eilenberg, Samuel,
Eilenberg, Samuel,
author_variant h c hc
h c hc
s e se
author_role VerfasserIn
VerfasserIn
VerfasserIn
author2 Buchsbaum, David A.,
Buchsbaum, David A.,
Eilenberg, Samuel,
Eilenberg, Samuel,
author2_variant d a b da dab
d a b da dab
s e se
author2_role MitwirkendeR
MitwirkendeR
VerfasserIn
VerfasserIn
author_sort Cartan, Henry,
title Homological Algebra (PMS-19), Volume 19 /
title_full Homological Algebra (PMS-19), Volume 19 / Henry Cartan, Samuel Eilenberg.
title_fullStr Homological Algebra (PMS-19), Volume 19 / Henry Cartan, Samuel Eilenberg.
title_full_unstemmed Homological Algebra (PMS-19), Volume 19 / Henry Cartan, Samuel Eilenberg.
title_auth Homological Algebra (PMS-19), Volume 19 /
title_alt Frontmatter --
Preface --
Contents --
Chapter I. Rings and Modules --
Chapter II. Additive Functors --
Chapter III. Satellites --
Chapter IV. Homology --
Chapter V. Derived Functors --
Chapter VI. Derived Functors of ⊗ and Hom --
Chapter VII. Integral Domains --
Chapter VIII. Augmented Rings --
Chapter IX. Associative Algebras --
Chapter X. Supplemented Algebras --
Chapter XI. Products --
Chapter XII. Finite Groups --
Chapter XIII. Lie Algebras --
Chapter XIV. Extensions --
Chapter XV. Spectral Sequences --
Chapter XVI. Applications of Spectral Sequences --
Chapter XVII. Hyperhomology --
Appendix: Exact Categories --
List o f Symbols --
Index o f Terminology
title_new Homological Algebra (PMS-19), Volume 19 /
title_sort homological algebra (pms-19), volume 19 /
series Princeton Mathematical Series ;
series2 Princeton Mathematical Series ;
publisher Princeton University Press,
publishDate 2016
physical 1 online resource (408 p.)
Issued also in print.
contents Frontmatter --
Preface --
Contents --
Chapter I. Rings and Modules --
Chapter II. Additive Functors --
Chapter III. Satellites --
Chapter IV. Homology --
Chapter V. Derived Functors --
Chapter VI. Derived Functors of ⊗ and Hom --
Chapter VII. Integral Domains --
Chapter VIII. Augmented Rings --
Chapter IX. Associative Algebras --
Chapter X. Supplemented Algebras --
Chapter XI. Products --
Chapter XII. Finite Groups --
Chapter XIII. Lie Algebras --
Chapter XIV. Extensions --
Chapter XV. Spectral Sequences --
Chapter XVI. Applications of Spectral Sequences --
Chapter XVII. Hyperhomology --
Appendix: Exact Categories --
List o f Symbols --
Index o f Terminology
isbn 9781400883844
9783110501063
9783110442496
9780691049915
callnumber-first Q - Science
callnumber-subject QA - Mathematics
callnumber-label QA611
callnumber-sort QA 3611
url https://doi.org/10.1515/9781400883844
https://www.degruyter.com/isbn/9781400883844
https://www.degruyter.com/document/cover/isbn/9781400883844/original
illustrated Not Illustrated
dewey-hundreds 500 - Science
dewey-tens 510 - Mathematics
dewey-ones 513 - Arithmetic
dewey-full 513.83
dewey-sort 3513.83
dewey-raw 513.83
dewey-search 513.83
doi_str_mv 10.1515/9781400883844
oclc_num 948780067
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hierarchy_parent_title Title is part of eBook package: De Gruyter Princeton Mathematical Series eBook Package
Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999
is_hierarchy_title Homological Algebra (PMS-19), Volume 19 /
container_title Title is part of eBook package: De Gruyter Princeton Mathematical Series eBook Package
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group.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Quotient module.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Right inverse.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Ring (mathematics).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Ring of integers.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Separation axiom.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Set (mathematics).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Special case.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Spectral sequence.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Subalgebra.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Subcategory.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Subgroup.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Subring.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Summation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Tensor product.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Theorem.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Topological space.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Topology.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Trivial representation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Unification (computer science).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Universal coefficient 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