This paper explores various homological regularity phenomena (in the sense of Auslander)
in category O and its several variations and generalizations. Additionally, we address the …

In this paper, we study certain properties of modules of finite Gorenstein projective, injective
and flat dimensions. We examine conditions which imply that all Gorenstein projective …

For finite modules over a local ring and complexes with finitely generated homology, we
consider several homological invariants sharing some basic properties with projective …

Let 𝒜 be an abelian category and 𝒳, 𝒴, 𝒵 additive full subcategories of 𝒜. We introduce and
study the Gorenstein category 𝒢 (𝒳, 𝒴, 𝒵) as a common generalization of some known …

The Chouinard formula for the injective dimension of a module over a noetherian ring is
extended to Gorenstein injective dimension. Specifically, if $ M $ is a module of finite …

We study the concepts of the 𝒫 C-projective and the ℐ C-injective dimensions of a module in
the noncommutative case, weakening the condition of C being semidualizing. We give the …

We study homotopy categories of model categories arising from a cotorsion triple, and the
equivalences between corresponding stable categories. We characterize homological …

Let Λ be a left and right noetherian ring and mod Λ the category of finitely generated left Λ-
modules. In this article, we show the following results.(1) For a positive integer k, the …

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 …

Let R be a left and right Noetherian ring and C a semidualizing R-bimodule. We introduce a
transpose Tr c M of an R-module M with respect to C which unifies the Auslander transpose …