It was proved by Beligiannis and Krause that over certain Artin algebras, there are
Gorenstein flat modules which are not direct limits of finitely generated Gorenstein projective …

In this paper, strongly Gorenstein flat modules are introduced and investigated. An R-
module M is called strongly Gorenstein flat if there is an exact sequence⋯→ P1→ P0→ P0→ …

We construct two examples of nonexcellent local Noetherian domains which demonstrate
that tight closure and completion do not commute. The first example is a local normal …

ABSTRACT Let R⊂ A be a Frobenius extension of rings. We prove that:(1) for any left A-
module M, AM is Gorenstein projective (injective) if and only if the underlying left R-module …

Over any associative ring $ R $ it is standard to derive $\mathrm {Hom} _R (-,-) $ using
projective resolutions in the first variable, or injective resolutions in the second variable, and …

Let R be a local ring and M a finitely generated R-module. The complete intersection
dimension of M–defined by Avramov, Gasharov and Peeva, and denoted–is a homological …

In this paper, we study Gorenstein projective and flat modules over a Noetherian ring R. For
an R-module M, we show that Gorenstein projective dimension of M is finite if and only if …

We construct a class of Gorenstein local rings R which admit minimal complete R-free
resolutions C such that the sequence {rank R Ci} is constant for i< 0, and grows …

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 certain properties of modules of finite Gorenstein projective, injective
and flat dimensions. We examine conditions which imply that all Gorenstein projective …