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 …

Let R be a ring such that (GP, GP⊥) forms a cotorsion pair cogenerated by a set, where GP
denotes the category of all Gorenstein projective R-modules. Recently, the first author …

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 …

We introduce and investigate Tate homology \rmtor of modules of finite Gorenstein flat
dimension. In particular, we show that over a right coherent ring R, \rmtor_i^R(M,N)≅ …

In this paper, we are concerned with Tate homology tor ̂ tor of modules of finite Gorenstein
FI-flat dimension. We determine connections between Tate, relative and absolute homology …

Motivated by some properties satisfied by Gorenstein projective and Gorenstein injective
modules over an Iwanaga-Gorenstein ring, we present the concept of left and right n …

Abstract We study Tate–Vogel cohomology of complexes by applying the model structure
induced by a complete hereditary cotorsion pair (A, B) of modules. Vanishing of Tate–Vogel …

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 …

Let (X, Y) be a balanced pair in an abelian category. We first introduce the notion of
cotorsion pairs relative to (X, Y), and then give some equivalent characterizations when a …

We define and study a notion of Gorenstein projective dimension for complexes of left
modules over associative rings. For complexes of finite Gorenstein projective dimension we …