This paper brings together two theories in algebra that have had been extensively
developed in recent years. First is the study of various homological dimensions and what …

In basic homological algebra, the projective, injective and flat dimensions of modules play
an important and fundamental role. In this paper, the closely related Gorenstein projective …

A new homological dimension, called G*-dimension, is defined for every finitely generated
module M over a local noetherian ring R. It is modeled on the CI-dimension of Avramov …

Given a semidualizing module C over a commutative Noetherian ring, Holm and Jørgensen
[Semi-dualizing modules and related Gorenstein homological dimensions, J. Pure Appl …

We present an alternative way of measuring the Gorenstein projective (resp., injective)
dimension of modules via a new type of complete projective (resp., injective) resolutions. As …

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 …

We introduce new homological dimensions, namely the Cohen-Macaulay projective,
injective and flat dimensions for homologically bounded complexes. Among other things we …

Let 𝒜 be an abelian category and (𝒳, 𝒴) a pair of classes of objects in 𝒜. Inspired by
Bouchiba's work on generalized Gorenstein projective modules, we give a new way of …

In this article, we investigate the change of rings theorems for the Gorenstein dimensions
over arbitrary rings. Namely, by the use of the notion of strongly Gorenstein modules, we …

A new homological dimension, called GCM-dimension, will be defined for any finitely
generated module M over a local Noetherian ring R. GCM-dimension (short for Generalized …