In basic homological algebra, projective, injective and flat modules play an important and
fundamental role. In this paper, we discuss some properties of Gorenstein projective …

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 …

Abstract The concept of Gorenstein Krull domains can be viewed as a Gorenstein analogue
of Krull domains, which are not necessarily integrally closed. This allows us to study those …

In this paper, we first study the Gorenstein projective/flat dimension of complexes of
modules. The relation between the Gorenstein projective/flat dimension for complexes and …

Let 𝒜 be an abelian category. In this paper, we investigate the global (𝒳, 𝒴)-Gorenstein
projective dimension gl. GPD (𝒳, 𝒴)(𝒜), associated to a GP-admissible pair (𝒳, 𝒴). We give …

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 …

We present an alternative way of measuring the Gorenstein projective (resp., injective)
dimension of modules via a new type of complete projective (resp., injective) resolutions. As …

Given a non-negative integer n and a ring R with identity, we construct a hereditary abelian
model structure on the category of left R-modules where the class of cofibrant objects …

Let S and R be rings and SCR a semidualizing bimodule. We investigate the relation
between the GC-syzygy with the C-syzygy of a module as well as the relation between the …

We prove that all Gorenstein projective modules are Gorenstein flat if and only each
Gorenstein projective module has finite Gorenstein flat dimension. As applications, some …