Rings with finite Gorenstein injective dimension
H Holm - Proceedings of the American Mathematical Society, 2004 - ams.org
H Holm
Proceedings of the American Mathematical Society, 2004•ams.orgIn this paper we prove that for any associative ring $ R $, and for any left $ R $-module $ M $
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 $ R $ is Gorenstein (provided
that $ R $ is commutative and Noetherian). References
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 $ R $ is Gorenstein (provided
that $ R $ is commutative and Noetherian). References
Abstract
In this paper we prove that for any associative ring , and for any left -module with finite projective dimension, the Gorenstein injective dimension equals the usual injective dimension . In particular, if is finite, then also is finite, and thus is Gorenstein (provided that is commutative and Noetherian). References
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