Gorenstein projective dimension with respect to a semidualizing module

Details Gorenstein projective dimension with respect to a semidualizing module Gorenstein projective dimension with respect to a semidualizing module

2006-11-22

arxiv.org/abs/math/0611711v2

Mathematics

Commutative Algebra

Final version, to appear in Journal of Commutative Algebra

Scientific paper

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 J{\o}rgensen'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.

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