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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The existence of finitely generated modules of finite Gorenstein injective dimension


Author: Ryo Takahashi
Journal: Proc. Amer. Math. Soc. 134 (2006), 3115-3121
MSC (2000): Primary 13D05; Secondary 13H10
Published electronically: May 12, 2006
MathSciNet review: 2231892
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Abstract: In this note, we study commutative Noetherian local rings having finitely generated modules of finite Gorenstein injective dimension. In particular, we consider whether such rings are Cohen-Macaulay.


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Additional Information

Ryo Takahashi
Affiliation: Department of Mathematics, Faculty of Science, Okayama University, 1-1, Naka 3-chome, Tsushima, Okayama 700-8530, Japan
Address at time of publication: Department of Mathematics, School of Science and Technology, Meiji University, 1-1-1 Higashimita, Tama-ku, Kawasaki 214-8571, Japan
Email: takahasi@math.okayama-u.ac.jp, takahasi@math.meiji.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08428-0
PII: S 0002-9939(06)08428-0
Keywords: G-injective dimension (Gorenstein injective dimension), G-dimension (Gorenstein dimension).
Received by editor(s): August 12, 2004
Received by editor(s) in revised form: October 1, 2004, January 31, 2005, and May 31, 2005
Published electronically: May 12, 2006
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2006 American Mathematical Society