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 (𝒳, 𝒴) be a complete and hereditary cotorsion pair in a bicomplete abelian category 𝒜.
We introduce a Gorenstein category 𝒢 (𝒳) and 𝒢 (𝒳)-resolution dimension of complexes …

In this paper, we introduce and study a notion of Gorenstein AC-injective dimension for
complexes of left modules over associative rings. We show first that the class of complexes …

Given two complete hereditary cotorsion pairs (Q, R) and (Q′, R′) in a bicomplete abelian
category G such that Q′⊆ Q and Q∩ R= Q′∩ R′, Becker showed that there exists a …

Let R be a right coherent ring and D b (R-Mod) the bounded derived category of left R-
modules. Denote by D^ b\left (R-Mod\right) _\left GF, C\right D b (R− M od) GF, C^ the …

Let R be a commutative Noetherian ring and C a semidualizing R-module. We obtain an
exact structure (ℋ C, 𝜀) and prove that the full subcategory ℋ C∩ 𝒢 ℱ C of ℋ C is a …

Let R be an associative ring with identity, and (A, B) a hereditary cotorsion pair generated by
a set in R-Mod. Then (dw A,(dw A)⊥) is a complete and hereditary cotorsion pair (we call it …

We study complete cohomology of complexes with finite Gorenstein AC-projective
dimension. We show first that the class of complexes admitting a complete level resolution is …

We study Tate-Vogel and relative cohomologies of complexes by applying the model
structure induced by a complete hereditary cotorsion pair ($\A $, $\B $) of modules. We show …

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 …