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Rings with finite Gorenstein injective dimension

Authors:	Henrik Holm

Affiliation:	Matematisk Afdeling, Københavns Universitet, Universitetsparken 5, 2100 Kobenhavn Ø, Danmark

Abstract:	In this paper we prove that for any associative ring , and for any left -module with finite projective dimension, the Gorenstein injective dimension $mathrm{Gid}_R M$ equals the usual injective dimension $mathrm{id}_R M$ . In particular, if $mathrm{Gid}_R R$ is finite, then also $mathrm{id}_R R$ is finite, and thus is Gorenstein (provided that is commutative and Noetherian).

Keywords:	Gorenstein dimensions homological dimensions Gorenstein rings

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