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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

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).
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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