University at Buffalo 3 credits Mathematics
The course is aimed at introducing students to homological algebra. Topics covered may include category-theoretic foundations, categories of complexes, resolutions, chain homotopy, projective/injective modules, tensor/symmetric/exterior algebras; semi-simple rings, Artin-Wedderburn theory, Jacobson radicals, basics on finite-group representation theory, Maschke’s Theorem; definition, examples and basic properties of derived functors, tor and ext as derived functors of tensor and hom functors, derivative notions such as flat/global ring/category dimensions, bicomplexes and tensor products of complexes, applications thereof to computing tor/ext.
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