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 ex1tends a result of Auslander and Bridger to rings of higher Krull dimension, and it also improves a result due to Fox1by where the ring is assumed to be CohenMacaulay.
| Original language | English |
|---|---|
| Pages (from-to) | 2265-2268 |
| Number of pages | 4 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 138 |
| Issue number | 7 |
| DOIs | |
| Publication status | Published - Jul 1 2010 |
Keywords
- (semi)dualizing module
- Cohen-Macaulay ring
- Gorenstein ring
- Injective dimension
- Projective dimension
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
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Takahashi, R., Yassemi, S., & Yoshino, Y. (2010). On the ex1istence of embeddings into modules of finite homological dimensions. Proceedings of the American Mathematical Society, 138(7), 2265-2268. https://doi.org/10.1090/S0002-9939-10-10323-2