… X is a class of modules that contains all projective modules. We show that the principal
results on Gorenstein projective module remain true for the X-Gorenstein projective modules. …

… Let X be a class of right R-modules that contains all projective right R-modules. The
notion of X-Gorenstein projective modules was introduced by D. Bennis and K. Ouarghi (…

… Let R be a ring, and let X be a projective class over R. An R-module M is called X-Gorenstein
projective if there exists an exact sequence of projective modules … GPR is a projective …

… In this paper, we intend to study relations of Gorenstein projective modules along Frobenius
extensions of rings. The theory of Frobenius extensions was developed by Kasch [15] as a …

… f −→ F −→ X −→ 0 with F free and X Gorenstein projective. Since M is finitely generated,
one can write F = P0 ⊕ Q0 with Imf ⊆ P0. Then we have an exact sequence 0 −→ M …

… Following [Mar2], we call a finite dimensional algebra nearly Gorenstein in case the Gorenstein
projective modules coincide with the stable modules and dually the Gorenstein injective …

… of X-Gorenstein projective modules. Section 3 deal with the … X-Gorenstein projective
modules In this section, we will review some properties of X-Gorenstein projective modules. The …

… If further Y contains all injective R-modules, we show the … We also show the existence
of X -Gorenstein projective … the classes of Gorenstein projective modules (denoted by GP(R)…

… concept of 𝒳-Gorenstein projective dimension for a complex M by its 𝒳-complete resolutions
in Section 3, where 𝒳 stands for a class of modules containing all projective modules (see …

… X Gorenstein AC-projective if there exists an exact complex of projective complexes … We
start with a classic result of Kaplansky [24] stating that every projective module is a direct sum of …