We study homological aspects of Gorenstein flat modules over a ring with respect to a
duality pair (L, A). These modules are defined as cycles of exact chain complexes with …

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 …

In this paper, we construct some model structures corresponding Gorenstein (ℒ, 𝒜)-modules
and relative Gorenstein flat modules associated to duality pairs, Frobenius pairs and …

For a $ k $-algebra $ A $, a quiver $ Q $, and an ideal $ I $ of $ kQ $ generated by monomial
relations, let $\Lambda:= A\otimes_k kQ/I $. We introduce the monic representations of $(Q …

For an integer N≥ 2 and three subcategories 𝒲, 𝒳, 𝒴 of modules, we study the notion of (𝒲,
𝒳, 𝒴)-Gorenstein N-complexes. We show that under certain hypotheses, an N-complex C is …

Let T be a right exact functor from an abelian category B into another abelian category A.
Then there exists an abelian category, named comma category and denoted by (T↓ A). In …

In this paper, we study the relationship of Gorenstein projective objects among three Abelian
categories in a recollement. As an application, we introduce the relation of $ n $-Gorenstein …

Let $ R $ be a ring, $\textrm {Proj} $ be the class of all projective right $ R $-modules,
$\mathcal K $ be the full subcategory of the homotopy category $\mathbf K (\textrm {Proj}) …

We introduce the notion of balanced pair of additive subcategories in an abelian category.
We give sufficient conditions under which a balanced pair of subcategories gives rise to a …

Let R be any ring with identity and Ch (R) C h (R) the category of chain complexes of (left) R-
modules. We show that the Gorenstein AC-projective chain complexes of 1 are the cofibrant …