By Cartan H., Eilenberg S.
Whilst this ebook used to be written, equipment of algebraic topology had triggered revolutions on the earth of natural algebra. to elucidate the advances that were made, Cartan and Eilenberg attempted to unify the fields and to build the framework of a completely fledged conception. The invasion of algebra had happened on 3 fronts during the development of cohomology theories for teams, Lie algebras, and associative algebras. This booklet provides a unmarried homology (and additionally cohomology) concept that embodies all 3; numerous effects is therefore tested in a common framework. thus, all of the 3 theories is singled out by way of an appropriate specialization, and its particular houses are studied.The place to begin is the concept of a module over a hoop. the first operations are the tensor manufactured from modules and the teams of all homomorphisms of 1 module into one other. From those, "higher order" derived of operations are acquired, which get pleasure from the entire homes often attributed to homology theories. This leads in a normal solution to the examine of "functors" and in their "derived functors.This mathematical masterpiece will attract all mathematicians operating in algebraic topology.
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Homological Algebra by Cartan H., Eilenberg S.