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 …

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 …

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 …

Let S and R be two associative rings, SCR be a faithfully balanced (S, R)-bimodule. We
introduce and investigate properties of∞-torsionfree modules with respect to SCR, which …

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 …

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 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 …

Auslander and Solberg introduced the concepts of finitely generated cotilting and tilting
modules in relative homological algebra considering subfunctors of the Ext-functor. In this …

We introduce a generalization of the Gorenstein injective modules: the Gorenstein FP n-
injective modules (denoted by GI n). They are the cycles of the exact complexes of injective …

Let R be a ring, C be a left R-module and S= End R (C). When C is semidualizing, the
Auslander class AC (S) and the Bass class ℬ C (R) associated with C have been the subject …