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 …

In this article, we give a new characterization of Gorenstein projective modules. As
applications of our result, we prove that a strongly Gorenstein projective module of …

We study approximations of modules of finite Gorenstein flat dimension by (projectively
coresolved) Gorenstein flat modules and modules of finite flat dimension. These …

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 …

A central problem in the theory of Gorenstein dimensions over commutative noetherian rings
is to find resolution-free characterizations of the modules for which these invariants are finite …

The classes of GC homological modules over commutative ring, where C is a semidualizing
module, extend Holm and J gensen's notions of C-Gorenstein homological modules to the …

We introduce a refinement of the Gorenstein flat dimension for complexes over an
associative ring—the Gorenstein flat-cotorsion dimension—and prove that it, unlike the …

For any group $ G $, the Gorenstein homological dimension ${\rm Ghd} _RG $ is defined to
be the Gorenstein flat dimension of the coefficient ring $ R $, which is considered as an …

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 …

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 …