2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/214006We 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.Final version, to appear in Journal of Commutative AlgebraCommutative AlgebraRings and Algebras13D02, 13D05, 13D07, 13D25, 18G20, 18G25text