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A characterization of modules locally of finite injective dimension


Author: Ryo Takahashi
Journal: Proc. Amer. Math. Soc. 135 (2007), 3461-3464
MSC (2000): Primary 13D05, 13D07
DOI: https://doi.org/10.1090/S0002-9939-07-08909-5
Published electronically: July 2, 2007
MathSciNet review: 2336558
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Abstract: In this note, we characterize finite modules locally of finite injective dimension over commutative Noetherian rings in terms of vanishing of Ext modules.


References [Enhancements On Off] (What's this?)

  • 1. BRUNS, W.; HERZOG, J. Cohen-Macaulay rings, revised edition. Cambridge Studies in Advanced Mathematics, 39. Cambridge University Press, Cambridge, 1998. MR 1251956 (95h:13020)
  • 2. GOTO, S. Vanishing of $ {\rm Ext}\sp{i}\sb{A}(M,\,A)$. J. Math. Kyoto Univ. 22 (1982/83), no. 3, 481-484. MR 674605 (84c:13019)
  • 3. MATSUMURA, H. Commutative ring theory. Translated from the Japanese by M. Reid. Cambridge Studies in Advanced Mathematics, 8. Cambridge University Press, Cambridge, 1986. MR 879273 (88h:13001)

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Additional Information

Ryo Takahashi
Affiliation: Department of Mathematics, School of Science and Technology, Meiji University, 1-1-1 Higashimita, Tama-ku, Kawasaki 214-8571, Japan
Email: takahasi@math.meiji.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-07-08909-5
Keywords: Injective dimension, Cohen-Macaulay locus
Received by editor(s): March 13, 2006
Received by editor(s) in revised form: August 19, 2006
Published electronically: July 2, 2007
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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