… 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)…

… with G-dimension zero, which generalized the class of finitely generated projective
modules … , and dually they defined Gorenstein injective modules. Beligiannis [5] defined X-Gorenstein …

… We point out that such objects generalize the usual Gorenstein projective … -projective,
Ding-injective, X -Gorenstein projective, Gorenstein AC-projective and G C -projective modules …

… Furthermore, we introduce the concept of ⊥ω-Gorenstein projective modules, and we
obtain that the relative Gorenstein projectivity is invariant under Frobenius extensions. …

… G is a bounded below complex of Gorenstein projective modules. If U ≃ V , where V is a
bounded above complex in which each module has finite projective dimension or finite injective …

… of Ding projective modules and … of projective modules and X is the subcategory of flat
modules, then (W , X , Y )-Gorenstein N-complexes above is particularly called Ding projective N-…

… (1) If V = W = Y = P(R), then G(V,W,Y,X) is just the class of X-Gorenstein projective
modules [6; 23]. In particular, when X = P(R) (resp. F(R), WF(R)), then G(V,W,Y,X) = GP(R) (resp. …

… if and only if every R-module has finite projective dimension; see Auslander and Buchsbaum
[3]. It is a crucial motivation for the study of homological dimensions of modules. In 1969, …

… every class X of modules over any ring, the class of X -Gorenstein Projective modules ( X - GP
) … Although submodules of projective modules need not be projective, Lemma 3.3 basically …

… stated, the notion of X -Gorenstein objects has already been … of Gorenstein projective and
Gorenstein injective modules into … projective modules and Add R ( C ) or injective modules and …