As a proper setting to study Gorenstein projective and injective dimensions of modules via
vanishing of Gorenstein Ext-functors, a notion of a generalized Gorenstein ring is introduced …

In this paper, we study Gorenstein injective, projective, and flat modules over a local Cohen-
Macaulay ring (R, m). We correspond to a dualizing module D of ˆR, the classes ΦD and ΨD …

En este Trabajo Fin de Máster desarrollamos varias ideas que nos han parecido
interesantes y que se enmarcan dentro de la teorıa del Algebra Homológica Relativa …

We discuss a class of modules, called test modules, that are, in principle, those detecting
finite homological dimensions. The main purpose of this mote is to report the following result …

Two classes of modules were studied: GI-flat and GF-torsion modules, where GI stands for
Gorenstein injective modules and GF for Gorenstein flat modules. Two homological …

Let (R, m, k) be a commutative Noetherian local ring. We examine various homological
dimensions of finitely generated Tor-rigid, test and testrigid, ie, both Tor-rigid and test …

Section 2 presents classical homological algebra in general algebraic terms. The classes of
projective modules, injective modules, and flat modules are defined, and the first two are …

Let $(R,{\frak {m}}, k) $ be a commutative Noetherian local ring. It is well-known that $ R $ is
regular if and only if the flat dimension of $ k $ is finite. In this paper, we show that $ R $ is …

Let R be a commutative Noetherian ring. There are several characterizations of Gorenstein
rings in terms of classical homological dimensions of their modules. In this paper, we use …