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 …

We prove that, if GProj is the class of all Gorenstein projective modules over a ring R, then
GP=(GProj, GProj⊥) is a cotorsion pair. Moreover, GP is complete when all projective …

The aim of this paper is twofold. On the one hand, we show that the dual Goldie dimension
codim (End (MR)) of the endomorphism ring End (MR) of a module MR can be used as a …

In this paper, we introduced two concepts. A module M is said to be purely quasi-injective
(resp. quasi-cotorsion) if it is fully invariant in its pure-injective envelope (resp. if it is flat and …

Let R be a commutative noetherian ring. We give criteria for a complex of cotorsion flat R-
modules to be minimal, in the sense that every self homotopy equivalence is an …

In this paper we give elementary lemmas on the vanishing of Tor and Ext for modules over a
commutative ring, which may be regarded as generalizations of known theorems on the …

Let R be a ring and na fixed non-negative integer. In this paper, n-weak cotorsion modules
are introduced and studied. A right R-module N is called n-weak cotorsion module if Ext …

Let $ R $ be a domain. It is proved that $ R $ is coherent when $ IFD (R)\lst1 $, and $ R $ is
Noetherian when $ IPD (R)\lst1 $. Consequently, $ R $ is a $ G $-Pr $\rm\ddot {u} $ fer …

We construct Abelian model structures on the category of chain complexes over a ring $ R $,
from the notion homological dimensions of modules. Given an integer $ n> 0$, we prove that …

A cotorsion theory is defined as a pair of classes Ext-orthogonal to each other. We give a
hereditary condition (HC) which is satisfied by the (flat, cotorsion) cotorsion theory and give …