On the existence of embeddings into modules of finite homological dimensions
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- by Ryo Takahashi, Siamak Yassemi and Yuji Yoshino PDF
- Proc. Amer. Math. Soc. 138 (2010), 2265-2268 Request permission
Abstract:
Let $R$ be a commutative Noetherian local ring. We show that $R$ is Gorenstein if and only if every finitely generated $R$-module can be embedded in a finitely generated $R$-module of finite projective dimension. This extends a result of Auslander and Bridger to rings of higher Krull dimension, and it also improves a result due to Foxby where the ring is assumed to be Cohen-Macaulay.References
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Additional Information
- Ryo Takahashi
- Affiliation: Department of Mathematical Sciences, Faculty of Science, Shinshu University, 3-1-1 Asahi, Matsumoto, Nagano 390-8621, Japan
- MR Author ID: 674867
- Email: takahasi@math.shinshu-u.ac.jp
- Siamak Yassemi
- Affiliation: Department of Mathematics, University of Tehran, P. O. Box 13145-448, Tehran, Iran – and – School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P. O. Box 19395-5746, Tehran, Iran
- MR Author ID: 352988
- Email: yassemi@ipm.ir
- Yuji Yoshino
- Affiliation: Graduate School of Natural Science and Technology, Okayama University, Okayama 700-8530, Japan
- Email: yoshino@math.okayama-u.ac.jp
- Received by editor(s): November 26, 2008
- Received by editor(s) in revised form: May 24, 2009
- Published electronically: February 23, 2010
- Additional Notes: The first and second authors were supported in part by Grant-in-Aid for Young Scientists (B) 19740008 from JSPS and by grant No. 88013211 from IPM, respectively
- Communicated by: Bernd Ulrich
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 2265-2268
- MSC (2010): Primary 13D05, 13H10
- DOI: https://doi.org/10.1090/S0002-9939-10-10323-2
- MathSciNet review: 2607854