Homological Algebra (PMS-19), Volume 19

Henry Cartan; Samuel Eilenberg

Published by Princeton University Press 1956

Homological Algebra (PMS-19), Volume 19

Henry Cartan and Samuel Eilenberg

In the series Princeton Mathematical Series

Volume 77 in the series Princeton Landmarks in Mathematics and Physics

https://doi.org/10.1515/9781400883844

Overview
Contents

About this book

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.

Author information

Henri Cartan, formerly Professor of Mathematics at the University of Paris, is a Fellow of the Royal Society. Samuel Eilenberg (1914-1998) was Professor of Mathematics at Columbia University. Both were founding members of the Bourbaki and both received the Wolf Prize in Mathematics.

Topics

Frontmatter Publicly Available Download PDF	i
Preface Requires Authentication Unlicensed Licensed Download PDF	v
Contents Publicly Available Download PDF	xi
Chapter I. Rings and Modules Requires Authentication Unlicensed Licensed Download PDF	1
Chapter II. Additive Functors Requires Authentication Unlicensed Licensed Download PDF	18
Chapter III. Satellites Requires Authentication Unlicensed Licensed Download PDF	33
Chapter IV. Homology Requires Authentication Unlicensed Licensed Download PDF	53
Chapter V. Derived Functors Requires Authentication Unlicensed Licensed Download PDF	75
Chapter VI. Derived Functors of ⊗ and Hom Requires Authentication Unlicensed Licensed Download PDF	106
Chapter VII. Integral Domains Requires Authentication Unlicensed Licensed Download PDF	127
Chapter VIII. Augmented Rings Requires Authentication Unlicensed Licensed Download PDF	143
Chapter IX. Associative Algebras Requires Authentication Unlicensed Licensed Download PDF	162
Chapter X. Supplemented Algebras Requires Authentication Unlicensed Licensed Download PDF	182
Chapter XI. Products Requires Authentication Unlicensed Licensed Download PDF	202
Chapter XII. Finite Groups Requires Authentication Unlicensed Licensed Download PDF	232
Chapter XIII. Lie Algebras Requires Authentication Unlicensed Licensed Download PDF	266
Chapter XIV. Extensions Requires Authentication Unlicensed Licensed Download PDF	289
Chapter XV. Spectral Sequences Requires Authentication Unlicensed Licensed Download PDF	315
Chapter XVI. Applications of Spectral Sequences Requires Authentication Unlicensed Licensed Download PDF	340
Chapter XVII. Hyperhomology Requires Authentication Unlicensed Licensed Download PDF	362
Appendix: Exact Categories David A. Buchsbaum Requires Authentication Unlicensed Licensed Download PDF	379
List o f Symbols Requires Authentication Unlicensed Licensed Download PDF	387
Index o f Terminology Requires Authentication Unlicensed Licensed Download PDF	389