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 …

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 …