Let R be a commutative ring, 𝒞 be a semidualizing R-module. We show that the Auslander
class 𝒜𝒞 (R) with respect to 𝒞 is the first left orthogonal class of some pure injective module …

Let R be a right perfect ring, and let (ℱ, 𝒞) be a cotorsion theory in the category of right R-
modules ℳ R. In this article, it is shown that every right R-module has a superfluous ℱ-cover …

Assume that (𝒜, ℬ) as well as (𝒞, 𝒟) form cotorsion theories of R-modules where R is an
integral domain. For R-modules A, B consider the R-module H= Hom R (A, B). Our main …

Let C be a semidualizing R-module, where R is a commutative ring. We first introduce the
definition of C-cotorsion modules, and obtain the properties of C-cotorsion modules. As …

Let R be a ring, M a right R-module, and na fixed non-negative integer. M is called n-
cotorsion if for any flat right R-module N. M is said to be n-flat if for any n-cotorsion right R …

Several authors have been interested in cotorsion theories. Among these theories we figure
the pairs $(\mathcal P_n,\mathcal P_n^{\perp}) $, where $\mathcal P_n $ designates the set …

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 …

nX-Projective Modules, nX-Injective Modules, Cotorsion Theories Page 1 Int. J. Contemp. Math.
Sciences, Vol. 5, 2010, no. 56, 2753 - 2762 n-X-Projective Modules, n-X-Injective Modules …

1. Introduction Throughout this paper, all rings are associative rings with units. For a ring R, we
use Mod R to denote the cate Page 1 EXTENSION CLOSURE OF ADJOINT COTORSIONFREE …

Let R be a ring (not necessarily commutative). A left R-module is said to be cotorsion if Ext 1
R (G, M)= 0 for any flat R-module G. It is well known that each pure-injective left R-module is …