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 …

We introduce a refinement of the Gorenstein flat dimension for complexes over an
associative ring—the Gorenstein flat-cotorsion dimension—and prove that it, unlike the …

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 …

In this paper, we prove that the global Gorenstein projective dimension of a ring $ R $ is
equal to the global Gorenstein injective dimension of $ R $ and that the global Gorenstein …

A central problem in the theory of Gorenstein dimensions over commutative noetherian rings
is to find resolution-free characterizations of the modules for which these invariants are finite …

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 …

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 …

In this paper, we study Gorenstein projective and flat modules over a Noetherian ring R. For
an R-module M, we show that Gorenstein projective dimension of M is finite if and only if …

In this note, we characterize the (weak) Gorenstein global dimension for arbitrary associative
rings. Also, we extend the well-known Hilbert's syzygy Theorem to the weak Gorenstein …

In this paper, we investigate the weak Gorenstein global dimension. We are mainly
interested in studying the problem when the left and right weak Gorenstein global …