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 …

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 …

If M is a nonzero finitely generated module over a commutative Noetherian local ring R such
that M has finite injective dimension and finite Gorenstein dimension, then it follows from a …

Let R be a Gorenstein ring. We prove that if I is an ideal of R such that R/I is a semi-simple
ring, then the Gorenstein flat dimension of R/I as a right R-module and the Gorenstein …

Unless stated otherwise, throughout this paper all rings are associative with identity and all
modules are unitary modules. Let R be a ring. We denote by R-Mod (Mod-R) the category of …

In this paper we prove that for any associative ring $ R $, and for any left $ R $-module $ M $
with finite projective dimension, the Gorenstein injective dimension $\mathrm {Gid} _R M …

Let $(R,\frak m, k) $ be a noetherian local ring. It is well-known that $ R $ is regular if and
only if the injective dimension of $ k $ is finite. In this paper it is shown that $ R $ is …

Let R be a ring and S an excellent extension of R. In this paper we study the Gorenstein
homological dimensions over R and S. We show that if M is an S-module, then MR is …