Year: 2006
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: White, Diana
Institution: University of South Carolina
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2952490718