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.
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© 2003 Professor P.M. Cohn
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Cohn, P.M. (2003). Homological Algebra. In: Further Algebra and Applications. Springer, London. https://doi.org/10.1007/978-1-4471-0039-3_2
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DOI: https://doi.org/10.1007/978-1-4471-0039-3_2
Publisher Name: Springer, London
Print ISBN: 978-1-4471-1120-7
Online ISBN: 978-1-4471-0039-3
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