We consider the following question: Is Gorenstein homology a X-pure homology, in the
sense defined by Warfield, for a class X of modules? Let GP denote the class of Gorenstein …

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 …

The principle “Every result in classical homological algebra should have a counterpart in
Gorenstein homological algebra” was given by Henrik Holm. There is a remarkable body of …

Let R be a commutative Noetherian ring, 𝔞 be an ideal of R and denote the derived category
of R-modules. We investigate the theory of local homology in conjunction with Gorenstein …

In this article we extend the notion of Gorenstein injective and projective modules to that of
complexes and characterize such complexes. We prove that over an n-Gorenstein ring every …

In this paper we assume that $ R $ is a Gorenstein Noetherian ring. We show that if
$(R,\mathfrak {m}) $ is also a local ring with Krull dimension $ d $ that is less than or equal to …

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 …

Let A be a noetherian local ring, xa non-unit element of A, B= A/(x). Let E be the Koszul
complex associated to an arbitrary set of generators of the ideal (x) of A. Assume that H1 (E) …

In the original paper on Gorenstein rings, Bass [1] characterizes Gorenstein rings as those
commutative Noetherian local rings A which are Cohen-Macaulay and satisfy nn {A)= 1 …

We give a sufficient condition for the class of Gorenstein injective modules be precovering: if
$ R $ is right noetherian and if the class of Gorenstein injective modules, $\mathcal {GI} $, is …