… We consider when the relative Gorenstein modules with respect to such a duality pair
coincide with the classical homological modules. As applications, we characterize (weak) global …

… singular compactness theorem which makes it possible to show that being a \(\Sigma \)-cotorsion
module is a property of the complete theory of the module. … of Gorenstein flat modules …

… Using the analogous approximations of Gorenstein flat modules by PGF-modules and flat
modules, that were obtained by Saroch and Stovicek in [26], we describe a similar Hovey triple …

… are the cycles of exact complexes of injective modules that stay exact when we … module A;
the Gorenstein AC-projective modules are the cycles of exact complexes of projective modules …

… Gorenstein homological algebra to any given semi-complete duality pair D = (L ,A ). This
generalizes the homological theory of the AC-Gorenstein modules … Ding injective modules are …

… (R) denote the subcategories of R-modules having flat and Gorenstein flat dimension less
than n ≥ 0. We call modules in these subcategories n-flat and n-Gorenstein flat, respectively. …

… modules and Gorenstein AC-projective modules (resp., absolutely clean modules and
Gorenstein AC-injective modules) … Štovıcek, Singular compactness and definability for Σ-cotorsion …

… E-Gorenstein injective and flat modules, respectively. We prove that a module is E-Gorenstein …
a direct summand of a strongly E-Gorenstein injective module, and every E-Gorenstein flat …

… We introduce the notion of Gorenstein flat left R-modules relative to a class B⊆ Mod (Rop) …
injective modules in Mod (Rop), every Gorenstein B-flat module is, in particular, Gorenstein flat…

… are special precovering, among them including the Gorenstein … Gorenstein flat PGF(R)
fulfils the same feature. We also introduce a new class of Gorenstein projective R-modules …