Homological Algebra (PMS-19), Volume 19

Couverture
Princeton University Press, 2 juin 2016 - 408 pages

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.

 

Pages sélectionnées

Table des matières

Chapter I Rings and Modules
3
Chapter II Additive Functors
18
Chapter III Satellites
33
Chapter IV Homology
53
Chapter V Derived Functors
75
Chapter VI Derived Functors of and Hom
106
Chapter VII Integral Domains
127
Chapter VIII Augmented Rings
143
Chapter XII Finite Groups
232
Chapter XIII Lie Algebras
266
Chapter XIV Extensions
289
Chapter XV Spectral Sequences
315
Chapter XVI Applications of Spectral Sequences
340
Chapter XVII Hyperhomology
362
Exact categories
379
List of Symbols
387

Chapter IX Associative Algebras
162
Chapter X Supplemented Algebras
182
Chapter XI Products
202
Index of Terminology
389
Droits d'auteur

Expressions et termes fréquents

A-projective apply associative assume augmentation called coincides Coker commutative diagram complex composition connecting homomorphisms Consequently consider contravariant convergent covariant defined definition denote differentiation direct sum double complex element epimorphism equivalent establish exact sequence Exer exists ExtA extension filtration finite follows formula functors further given graded HomA homology homomorphism homotopy Homr Horn Horn A,C ideal identified identity II-module implies induced injective integer invariant isomorphism K-algebra left A-module left exact Lie algebra module monomorphism morphism multiplication natural obtain operators particular projective resolution Proof properties Proposition prove regarded relation replaced respect right A-module ring satisfies setting similar Similarly situation spectral sequences splits subgroup submodule suffices supplemented Theorem theory two-sided unique variables weakly yields Z(II zero

À propos de l'auteur (2016)

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.

Informations bibliographiques

TitreHomological Algebra (PMS-19), Volume 19
Volume 37 de Princeton Mathematical Series
Volume 28 de Princeton Landmarks in Mathematics and Physics
AuteursHenri Cartan, Samuel Eilenberg
ÉditeurPrinceton University Press, 2016
ISBN1400883849, 9781400883844
Longueur408 pages
  
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