Abstract
Let A be a finite-dimensional k-algebra (associative, with unit) over some fixed algebraically closed field k. Let mod A be the category of finitely generated left A-modules. With D = Homk(—,k) we denote the standard duality with respect to the ground field. Then A D(A A) is an injective cogenerator for mod A. For an arbitrary A-module A X we denote by proj.dimA X (resp. inj.dimA X) the projective dimension (resp. the injective dimension) of the module A X.
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Happel, D. (1991). On Gorenstein Algebras. In: Michler, G.O., Ringel, C.M. (eds) Representation Theory of Finite Groups and Finite-Dimensional Algebras. Progress in Mathematics, vol 95. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8658-1_16
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DOI: https://doi.org/10.1007/978-3-0348-8658-1_16
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