We introduce the concepts of generalized compatible and cocompatible bimodules in order
to characterize Gorenstein projective, injective and flat modules over trivial ring extensions …

We construct new complete cotorsion pairs in the categories of modules and chain
complexes over a Gorenstein ring $ R $, from the notions of Gorenstein homological …

Let R be a ring such that all flat R-modules have finite strongly FP-injective dimension. We
obtain that the class of all Gorenstein projective modules forms a left-hand class of complete …

Let R be a ring, M a right R-module, and na fixed non-negative integer. M is called n-
cotorsion if for any flat right R-module N. M is said to be n-flat if for any n-cotorsion right R …

We describe the structure of finitely generated cotorsion modules over commutative
noetherian rings. Also we characterize the so-called covering morphisms between finitely …

We characterize Ding modules and complexes over Ding-Chen rings. We show that, over a
Ding-Chen ring R, the Ding projective (respectively, Ding injective, respectively, Ding flat) R …

Assume that the class of all Gorenstein (ℒ, 𝒜)-flat modules is closed under extensions. We
define a notion of Gorenstein (ℒ, 𝒜)-flat dimension for complexes and consider equivalent …

Let X and Y be N-complexes with N≥ 2 an integer such that X has finite Gorenstein
projective dimension and Y has finite Gorenstein injective dimension. We define the n th …

We study homological and homotopical aspects of Gorenstein flat modules over a ring with
respect to a duality pair $(\mathcal {L, A}) $. These modules are defined as cycles of exact …

Given a ring $ R $, two classes $\mathcal A $ and $\mathcal B $ of $ R $-modules are said
to form a cotorsion pair $(\mathcal A,\mathcal B) $ in $\operatorname {Mod} R $ if $\mathcal …