## Rings with finite Gorenstein injective dimension

Research output: Contribution to journal › Journal article › Research › peer-review

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**Rings with finite Gorenstein injective dimension.** / Holm, Henrik Granau.

Research output: Contribution to journal › Journal article › Research › peer-review

#### Harvard

*Proceedings of the American Mathematical Society*, vol. 132, no. 5, pp. 1279-1283.

#### APA

*Proceedings of the American Mathematical Society*,

*132*(5), 1279-1283.

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#### Bibtex

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#### RIS

TY - JOUR

T1 - Rings with finite Gorenstein injective dimension

AU - Holm, Henrik Granau

PY - 2004

Y1 - 2004

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

VL - 132

SP - 1279

EP - 1283

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 5

ER -

ID: 41927917