Gorenstein projective dimension with respect to a semidualizing module
| dc.creator | White, Diana | |
| dc.date | 2006-11-22 | |
| dc.date | 2009-01-02 | |
| dc.date.accessioned | 2026-07-07T12:23:29Z | |
| dc.date.available | 2026-07-07T12:23:29Z | |
| dc.description | We introduce and investigate the notion of $\gc$-projective modules over (possibly non-noetherian) commutative rings, where $C$ is a semidualizing module. This extends Holm and Jørgensen's notion of $C$-Gorenstein projective modules to the non-noetherian setting and generalizes projective and Gorenstein projective modules within this setting. We then study the resulting modules of finite $\gc$-projective dimension, showing in particular that they admit $\gc$-projective approximations, a generalization of the maximal Cohen-Macaulay approximations of Auslander and Buchweitz. Over a local (noetherian) ring, we provide necessary and sufficient conditions for a $G_C$-approximation to be minimal. | |
| dc.description | Final version, to appear in Journal of Commutative Algebra | |
| dc.identifier | https://arxiv.org/abs/math/0611711 | |
| dc.identifier | http://arxiv.org/abs/math/0611711 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/214006 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Rings and Algebras | |
| dc.subject | 13D02, 13D05, 13D07, 13D25, 18G20, 18G25 | |
| dc.title | Gorenstein projective dimension with respect to a semidualizing module | |
| dc.type | text |