Ext and Tor
Homological algebra, the study of homology groups and related constructions, was a branch of algebraic topology until Eilenberg and MacLane  devised a purely algebraic cohomology of groups, which shared many features with the cohomology of topological spaces. Recognition as a separate branch of algebra came with the book Homological Algebra , by Cartan and Eilenberg. This chapter contains the basic properties of homology groups, resolutions, Ext, and Tor, with applications to groups and rings. As before, all rings have an identity element, and all modules are unital.
KeywordsAbelian Group Exact Sequence Commutative Diagram Short Exact Sequence Natural Isomorphism
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