We introduce the notion of a duality pair and demonstrate how the left half of such a pair is"
often" covering and preenveloping. As an application, we generalize a result by Enochs et …

We introduce a refinement of the Gorenstein flat dimension for complexes over an
associative ring—the Gorenstein flat-cotorsion dimension—and prove that it, unlike the …

Let A be an abelian category. A subcategory X of A is called a resolving subcategory if X is
closed under extensions and kernels of epimorphisms and contains all projective objects of …

Let C be a semidualizing module over a commutative noetherian ring R. We exhibit an
isomorphism Tor^F_CM_i(-,-)≅Tor^P_CM_i(-,-) between the bifunctors defined via C-flat and …

A model structure on a category is a formal way of introducing a homotopy theory on that
category, and if the model structure is abelian and hereditary, its homotopy category is …

Sather-Wagstaff et al. proved in [8](S. Sather-Wagsta, T. Sharif and D. White, Stability of
Gorenstein categories, J. Lond. Math. Soc.(2), 77 (2)(2008), 481–502) that iterating the …

A left R-module M is called two-degree Gorenstein flat if there exists an exact sequence of
Gorenstein flat left R-modules⋅⋅⋅→ G2→ G1→ G0→ G− 1→ G− 2→⋅⋅⋅ such that M≅ Ker …

The theory of Gorenstein flat dimension is not complete since it is not yet known whether the
category 𝒢ℱ (R) of Gorenstein flat modules over a ring R is projectively resolving or not …

In this paper, we give a relationship between projective generators (resp., injective
cogenerators) in the category of R-modules and the counterparts in the category of …

To investigate cohomology theories based on flats, Asadollahi and Salarian gave the
definition of F-Gorenstein flat R-modules, and these modules are exactly Gorenstein flat …