This paper discusses a variant theory for the Gorenstein flat dimension. Actually, since it is
not yet known whether the category GF (R) of Gorenstein flat modules over a ring R is …

The theory of Gorenstein flat dimension is not complete since it is not yet known whether the
category 𝒢ℱ (R) of Gorenstein flat modules over a ring R is projectively resolving or not …

Throughout this paper, if not specified otherwise, R denotes an associative ring with identity
and all modules are unital left R-modules. Every result given for left modules has a …

Unlike the Gorenstein projective and injective dimensions, the majority of results on the
Gorenstein flat dimension have been established only over Noetherian (or coherent) rings …

It is well known that, given a ring R, if M is an R-module such that pdR (M)<∞, then GidR
(M)= idR (M)(Holm, 2004). This shows in particular that if R is a Noetherian ring such that …

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 …

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 …

This article is concerned with the strongly Gorenstein flat dimensions of modules and rings.
We show this dimension has nice properties when the ring is coherent, and extend the well …

In this paper we characterize the relative Gorenstein weak global dimension of the
generalized Gorenstein $\mathcal {Y} $-flat modules recently studied by S. Estrada, A. Iacob …

In this paper, we study Gorenstein injective, projective, and flat dimensions over a Cohen-
Macaulay local ring R admitting a dualizing module. In particular, we characterize these …