Abstract Let 𝒱, 𝒲, 𝒴, 𝒳 be four classes of modules. We introduce a notion of (𝒱, 𝒲, 𝒴, 𝒳)-
Gorenstein modules which unifies a number of well-known Gorenstein modules. Under …

In order to establish the Foxby equivalences associated to strongly Gorenstein modules, we
introduce the notions of strongly WP-Gorenstein, WI-Gorenstein and WF-Gorenstein …

This paper introduces and studies (X, Y)-Gorenstein projective and injective modules, which
are a generalization of Enochs' Gorenstein projective and injective modules, respectively …

In this paper, we generalize the notion of Gorenstein projective modules. Namely, we
introduce X-Gorenstein projective modules, where X is a class of modules that contains all …

We introduce the notion of Gorenstein star modules and obtain some properties and a
characterization of them. We mainly give the relationship between n-Gorenstein star …

Abstract Let R⊂ S be a Frobenius extension of rings and M a left S-module and let 𝓧 be a
class of left R-modules and 𝒚 a class of left S-modules. Under some conditions it is proven …

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 (X-Gorenstein …

Let $\mathcal {V} $, $\mathcal {W} $, $\mathcal {Y} $, $\mathcal {X} $ be four classes of left $
R $-modules. The notion of $(\mathcal {V, W, Y, X}) $-Gorenstein $ R $-complexes is …

Gorenstein injective, projective and coflat comodules were introduced and studied by
Asensio and Enochs et al. We further investigate these comodules and introduce n …

The authors introduce and investigate the T_C-Gorenstein projective, L_C-Gorenstein
injective and H_C-Gorenstein flat modules with respect to a semidualizing module C which …