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 |
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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 2010 |
Externally published | Yes |
Keywords
- (semi)dualizing module
- Cohen-Macaulay ring
- Gorenstein ring
- Injective dimension
- Projective dimension
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics