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Homological Algebra (PMS-19).

Author: Henry Cartan
Publisher: Princeton University Press, 2016.
Series: Princeton Mathematical Series, 19
Edition/Format:   eBook : Document : English
Summary:
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  Read more...
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Details

Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Henry Cartan
ISBN: 1400883849 9781400883844
OCLC Number: 948780067
Language Note: In English.
Description: 1 online resource
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
Series Title: Princeton Mathematical Series, 19
More information:

Abstract:

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.

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