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 …

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 …

In this paper, Gorenstein FP-injective modules are introduced and studied. An R-module M
is called Gorenstein FP-injective if there is an exact sequence⋯→ E1→ E0→ E0→ E1→⋯ of …

We prove that for a Frobenius extension, if a module over the extension ring is Gorenstein
projective, then its underlying module over the base ring is Gorenstein projective; the …

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 …

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 …

Journal of Algebra Strongly Gorenstein projective, injective and flat modules Page 1 Journal
of Algebra 320 (2008) 2659–2674 Contents lists available at ScienceDirect Journal of Algebra …

Let ℰ be an injectively resolving subcategory of left R-modules. We study a particular case of
ℰ-Gorenstein injective and flat modules, called strongly ℰ-Gorenstein injective and flat …

This article continues to investigate a particular case of Gorenstein FP-injective modules,
called strongly Gorenstein FP-injective modules. Some examples are given to show that …

In this article, we study the relation between m-strongly Gorenstein projective (resp.,
injective) modules and n-strongly Gorenstein projective (resp., injective) modules whenever …