We introduce a notion of total acyclicity associated to a subcategory of an abelian category
and consider the Gorenstein objects they define. These Gorenstein objects form a Frobenius …

We present and study the concept of m-periodic Gorenstein objects relative to a pair (A, B) of
classes of objects in an abelian category, as a generalization of m-strongly Gorenstein …

In this paper we study a generalisation of the Igusa-Todorov functions which gives rise to a
vast class of algebras satisfying the finitistic dimension conjecture. This class of algebras is …

Let 𝒜 be an abelian category. In this paper, we investigate the global (𝒳, 𝒴)-Gorenstein
projective dimension gl. GPD (𝒳, 𝒴)(𝒜), associated to a GP-admissible pair (𝒳, 𝒴). We give …

In this paper we introduce a special kind of relative (co) resolutions associated to a pair of
classes of objects in an abelian category $\mathcal {C}. $ We will see that, by studying these …

Let (A, B) be a GP-admissible pair and (Z, W) be a GI-admissible pair of classes of objects in
an abelian category C, and consider the class π GP (ω, B, 1) of 1-periodic (ω, B)-Gorenstein …

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 …

In this paper, we prove that for a $ n $-perfect ring $ R $ various classes of relative
Gorenstein projective $ R $-modules are special precovering, among them including the …

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 …

Let $(\mathcal {A, B}) $ be a GP-admissible pair and $(\mathcal {Z, W}) $ be a GI-admissible
pair of classes of objects in an abelian category $\mathcal {C} $, and consider the class …