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 …

Given a ring $ R $, two classes $\mathcal A $ and $\mathcal B $ of $ R $-modules are said
to form a cotorsion pair $(\mathcal A,\mathcal B) $ in $\operatorname {Mod} R $ if $\mathcal …

We consider the perfect cotorsion pair (𝒫1, 𝒟) over a commutative ring (often over a domain)
R consisting of modules of projective dimension≤ 1 and of divisible modules, respectively …

Let R be a ring, na fixed non-negative integer and ℱ ℐ n (ℱ n) the class of all right (left) R-
modules of FP-injective (flat) dimension at most n. We prove that (is a perfect cotorsion …

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 …

Let R be a left Noetherian ring, S a right Noetherian ring and RU a generalized tilting
module with S= End (RU). We give some equivalent conditions that the injective dimension …

Let R be a ring. A right R-module M is called f-projective if Ext1 (M, N)= 0 for any f-injective
right R-module N. We prove that (F-proj, F-inj) is a complete cotorsion theory, where F-proj …

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 …

In basic homological algebra, the flat and injective dimensions of modules play an important
and fundamental role. In this paper, the closely related IFP-flat and IFP-injective dimensions …

In this paper, we study the class of complexes of FP-injective left R-modules. It is shown that
the pair is a complete cotorsion pair. If R is a left coherent ring, it is proved that every …