In this paper we develop the homological properties of the $(\mathcal {L},\mathcal {A}) $-
Gorenstein flat $ R $-modules $\mathcal {GF} _ {(\mathcal {F}(R),\mathcal {A})} $ proposed …

In this paper, we prove that the Gorenstein analogue of the well-known Auslander's theorem
on the global dimension holds true. Namely, we prove that the Gorenstein global dimension …

In this paper we introduce and study the weak Gorenstein global dimension of a ring $ R $
with respect to a left $ R $-module $ C $. We provide several characterizations of when this …

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 …

For any group $ G $, the Gorenstein homological dimension ${\rm Ghd} _RG $ is defined to
be the Gorenstein flat dimension of the coefficient ring $ R $, which is considered as an …

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 …

The study of global dimension of pullback rings has been subject of several interesting
works and has been served to solve many open problems. In this paper, we attempt to …

We show that over a right coherent left perfect ring R, a complex C of left R-modules is
Gorenstein projective if and only if C m is Gorenstein projective in R-Mod for all m∈ ℤ …

Let be an ideal of ad-dimensional Gorenstein ring $ R $ and let $ M $ be an $ R $-module of
finite projective dimension. In this paper, among the other things, we show that, for every $ R …