Homological Algebra

P. M. Cohn
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P. M. Cohn: University College London, Department of Mathematics

Chapter 2 in Further Algebra and Applications, 2003, pp 33-89 from Springer

Abstract: Abstract The present chapter serves as a concise introduction to homological algebra. Only the basic notions of category theory (treated in BA) are assumed. The definition of abelian categories (Section 2.1) and of functors between them (Section 2.2) is followed by an abstract description of module categories in Section 2.3. A study of resolutions leads to the notion of homological dimension in Section 2.4; derived functors are then defined in Section 2.5 and exemplified in Section 2.6 by the instances that are basic for rings, Ext and Tor. Universal derivations are used in Section 2.7 to prove a form of Hilbert’s syzygy theorem.

Keywords: Exact Sequence; Direct Summand; Short Exact Sequence; Additive Category; Abelian Category (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1007/978-1-4471-0039-3_2

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