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 …

We study homological and homotopical aspects of Gorenstein flat modules over a ring with
respect to a duality pair $(\mathcal {L, A}) $. These modules are defined as cycles of exact …

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 …

Let $(\mathcal {A, B}) $ be a GP-admissible pair and $(\mathcal {Z, W}) $ be a GI-admissible
pair of classes of objects in an abelian category $\mathcal {C} $, and consider the class …

We extend the notion of virtually Gorenstein rings to the setting of arbitrary rings, and prove
that all rings R of finite Gorenstein weak global dimension are virtually Gorenstein such that …

Enochs and Jenda gave some characterizations of Gorenstein injective and projective
complexes over n-Gorenstein rings. The aim of this article is to generalize these results and …

In this paper we study the finiteness of global Gorenstein AC-homological dimensions for
rings, and answer the questions posed by Becerril, Mendoza, Pérez and Santiago. As an …

In this paper, we study the relative homological dimension based on the class of projectively
coresolved Gorenstein flat modules (PGF-modules), that were introduced by Saroch and …

In this paper we mainly study the homological properties of dual modules over k-Gorenstein
rings. For a right quasi k-Gorenstein ring Λ, we show that the right self-injective dimension of …

Let R be a commutative Noetherian ring. The aim of this paper is studying the properties of
relative Gorenstein modules with respect to a dualizing module. It is shown that every …