Homological Algebra
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€117.99
A01=Henri Cartan
A01=Samuel Eilenberg
Abelian group
Algebra homomorphism
Algebraic topology
Associative algebra
Author_Henri Cartan
Author_Samuel Eilenberg
Axiom
Category of modules
Category=PBF
Cohomology
Cokernel
Commutative diagram
Commutative property
Commutative ring
Derived functor
Diagram (category theory)
Differential operator
Direct product
Direct sum
Duality (mathematics)
Endomorphism
Epimorphism
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equivalence class
Exact category
Exact sequence
Explicit formulae (L-function)
Finitely generated module
Free abelian group
Functor
Fundamental group
Galois theory
Global dimension
Group algebra
Hereditary ring
Hochschild homology
Homological algebra
Homology (mathematics)
Homomorphism
Homotopy
Hyperhomology
Ideal (ring theory)
Inclusion map
Induced homomorphism
Injective module
Integral domain
Inverse limit
Lie algebra
Linear differential equation
Mathematical induction
Module (mathematics)
Monoidal category
Noetherian
Noetherian ring
Pontryagin duality
Product topology
Projective module
Quotient algebra
Quotient module
Right inverse
Ring (mathematics)
Set (mathematics)
Special case
Spectral sequence
Subalgebra
Subcategory
Tensor product
Theorem
Topological space
Topology
Unification (computer science)
Universal coefficient theorem
Variable (mathematics)
Zero object (algebra)
Product details
- ISBN 9780691049915
- Weight: 539g
- Dimensions: 197 x 254mm
- Publication Date: 19 Dec 1999
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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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.
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.
