For any group G and any commutative ring R, the Gorenstein homological dimension
GhdRG, defined as the Gorenstein flat dimension of the trivial RG-module R, 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 …

In this paper, we introduce and study the projectively coresolved Gorenstein flat dimension
of a group G over a commutative ring R and we prove that this dimension enjoys all the …

Let $ G $ be a group and $ R $ be a ring. We define the Gorenstein homological dimension
of $ G $ over $ R $, denoted by ${\rm Ghd} _ {R} G $, as the Gorenstein flat dimension of …

Projectively coresolved Gorenstein flat modules were introduced by Saroch and Stovicek
and were shown to be Gorenstein projective. We give characterizations of Gorenstein …

In this paper, we study finiteness criteria for the Gorenstein homological dimension of groups
over a commutative ring of finite weak Gorenstein global dimension and provide good …

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 mainly investigate the $\mathfrak {X} $-Gorenstein projective dimension of
modules and the (left) $\mathfrak {X} $-Gorenstein global dimension of rings. Some …

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 …

Let $(R,\m) $ be a commutative noetherian local ring and let $\Gamma $ be a finite group. It
is proved that if $ R $ admits a dualizing module, then the group ring $ R\ga $ has a …