Rings with finite Gorenstein injective dimension

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In this paper we prove that for any associative ring R, and for any left R-module M with nite projective dimension, the Gorenstein injective dimension GidRM equals the usual injective dimension idRM. In particular, if GidRR is nite, then also idRR is nite, and thus R is Gorenstein (provided that R is commutative and Noetherian).
Original languageEnglish
JournalProceedings of the American Mathematical Society
Issue number5
Pages (from-to)1279-1283
Publication statusPublished - 2004

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