Rings with finite Gorenstein injective dimension
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- by Henrik Holm
- Proc. Amer. Math. Soc. 132 (2004), 1279-1283
- DOI: https://doi.org/10.1090/S0002-9939-03-07466-5
- Published electronically: November 7, 2003
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Abstract:
In 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
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Bibliographic Information
- Henrik Holm
- Affiliation: Matematisk Afdeling, Københavns Universitet, Universitetsparken 5, 2100 København Ø, Danmark
- Email: holm@math.ku.dk
- Received by editor(s): January 28, 2003
- Published electronically: November 7, 2003
- Communicated by: Bernd Ulrich
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 1279-1283
- MSC (2000): Primary 13D02, 13D05, 13D07, 13H10; Secondary 16E05, 16E10, 16E30
- DOI: https://doi.org/10.1090/S0002-9939-03-07466-5
- MathSciNet review: 2053331