Homological Algebra

Front Cover
Princeton University Press, 1999 - Mathematics - 390 pages
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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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Contents

II
3
III
18
IV
33
V
53
VI
75
VII
106
VIII
127
IX
143
XIII
232
XIV
266
XV
289
XVI
315
XVII
340
XVIII
362
XIX
379
XX
387

X
162
XI
182
XII
202

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Algebra
Serge Lang
Limited preview - 2002
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