Rings with finite Gorenstein injective dimension

Henrik Granau Holm

Rings with finite Gorenstein injective dimension

42 Citationer (Scopus)

550 Downloads (Pure)

Abstract

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).

Originalsprog	Engelsk
Tidsskrift	Proceedings of the American Mathematical Society
Vol/bind	132
Udgave nummer	5
Sider (fra-til)	1279-1283
ISSN	0002-9939
Status	Udgivet - 2004

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Citationsformater

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T1 - Rings with finite Gorenstein injective dimension

AU - Holm, Henrik Granau

PY - 2004

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N2 - 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).

AB - 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).

M3 - Journal article

SN - 0002-9939

VL - 132

SP - 1279

EP - 1283

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 5

ER -