The main purpose of this article is to present some applications of the notion of Gorenstein
injective dimension of complexes over an associative ring. Among the applications, we give …

In this paper we characterize the relative Gorenstein weak global dimension of the
generalized Gorenstein $\mathcal {Y} $-flat modules recently studied by S. Estrada, A. Iacob …

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 …

In this article, we prove that Gorenstein projectivity and injectivity with respect to a
semidualizing module are preserved under Frobenius extensions. Furthermore, we obtain …

This paper brings together two theories in algebra that have had been extensively
developed in recent years. First is the study of various homological dimensions and what …

Assume that the class of all Gorenstein (ℒ, 𝒜)-flat modules is closed under extensions. We
define a notion of Gorenstein (ℒ, 𝒜)-flat dimension for complexes and consider equivalent …

Let $ I $ be an integrally closed ideal in a commutative Noetherian ring $ A $. Then the local
ring $ A_ {\mathfrak {p}} $ is regular (resp. Gorenstein) for every $\mathfrak {p}\in\mathrm …

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 …

Let R be a ring. A left R-module M is called GI-injective if for any Gorenstein injective left R-
module N. It is shown that a left R-module M over any ring R is GI-injective if and only if M is …

In this article, we investigate the Gorenstein global dimension with respect to the
recollements of abelian categories. With the invariants spli and silp of the categories, we …