Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Rings with finite Gorenstein injective dimension

Author(s): Henrik Holm
Journal: Proc. Amer. Math. Soc. 132 (2004), 1279-1283.
MSC (2000): Primary 13D02, 13D05, 13D07, 13H10; Secondary 16E05, 16E10, 16E30
Posted: November 7, 2003
MathSciNet review: 2053331
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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).

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