For a left Noetherian ring R, if the supremum of flat dimensions of all injective left R-modules
is finite, we prove that strongly cotorsion left R-modules coincide with Gorenstein injective …

In this note, it is proven that if R is a right noetherian ring with id R o R<∞ and E xt R i≥ 1
(M, F)= 0 for any left R-module F with finite flat dimension, then M is Gorenstein projective; if …

By investigating the properties of some special covers and envelopes of modules, we prove
that if R is a Gorenstein ring with the injective envelope of RR flat, then a left R-module is …

We prove that the class of Gorenstein injective modules is both enveloping and covering
over a two sided noetherian ring such that the character modules of Gorenstein injective …

Let be a left Noetherian ring satisfying the Auslander condition. It is proven that a left-module
is Gorenstein injective if and only if is strongly cotorsion and for any injective left-module; a …

We study homological behavior of modules satisfying the Auslander condition. Assume that
AC is the class of left R-modules satisfying the Auslander condition. It is proved that each …

Let R be a ring and let 𝒮𝒢ℱ be the class of strongly Gorenstein at right R-modules. We call a
right R-module M a weak Gorenstein cotorsion module if M is in the class 𝒮𝒢ℱ⊥. Properties …

A left and right Noetherian ringRis called Gorenstein if bothRRandRRhave finite injective
dimensions. These rings were studied by Bass for the commutative case and Iwanaga for …

In this paper, we study Gorenstein injective modules over a local Noetherian ring R. For an
R-module M, we show that M is Gorenstein injective if and only if Hom R (Ȓ, M) belongs to …

A complex C is called Gorenstein injective if there exists an exact sequence of
complexes⋯→ I− 1→ I0→ I1→⋯ such that each Ii is injective, C= Ker (I0→ I1) and the …