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 …

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)≅ …

Given two complete hereditary cotorsion pairs (𝒬, ℛ) and (𝒬′, ℛ′) in the category of
modules which satisfy the conditions 𝒬′⊆ 𝒬, 𝒬∩ ℛ= 𝒬′∩ ℛ′, and ℛ′ is enveloping, a …

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In this article, we introduce and study the Gorenstein cotorsion dimension of modules and
rings. It is shown that this dimension has nice properties when the ring in question is left GF …

Let $ R $ be a left coherent ring. It is proven that if an $ R $-module $ M $ has a finite FP-
injective dimension, then the Gorenstein projective (resp. Gorenstein flat) dimension and 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 …

We define a notion of Gorenstein flat dimension for unbounded complexes over left GF-
closed rings. Over Gorenstein rings we introduce a notion of Gorenstein cohomology for …

In this article, we define and study a notion of strongly Gorenstein flat dimensions for
complexes of left modules over associative rings. In particular, we consider the class of …

In this paper, we study when the kernel of a complete hereditary cotorsion pair is the additive
closure of a tilting module. Applications go in three directions. The first is to characterize …