Let $ R $ be a ring with identity and let $\mathcal {M} _R $ be the category of right $ R $-
modules. In this article, we study some relations between torsion theories and cotorsion …

Let R be a ring. A right R-module C is called cotorsion if for any flat right R-module biF. In
this paper, we first give some results on cotorsion envelopes that are analogous to those on …

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 …

Cotorsion theories Page 1 Pacific Journal of Mathematics COTORSION THEORIES STEPHEN
DALE BRONN Vol. 48, No. 2 April 1973 Page 2 PACIFIC JOURNAL OF MATHEMATICS Vol …

Let R be a ring. A right R-module C is called a cotorsion module if Ext1R (F, C)= 0 for any flat
right R-module F. In this paper, we first characterize those rings satisfying the condition that …

Let τ be a hereditary torsion theory on the category R-mod of left modules over an
associative unitary ring R. We will study the τ-injective hull of certain modules, giving an …

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 ring with identity. In this note we study covers of left R-modules by r-injectives left
R-modules, where r is a hereditary torsion theory defined in the category of all left R …

A right R-module M is torsion-free (in the sense of Hattori) if for all r∈ R. The class of torsion-
free modules is a cotilting class if and only if R is a left pp-ring. This paper investigates how …

Using SE Dickson's characterization of a torsion class, a class of modules closed under
taking factors extensions and arbitrary direct sum, we study torsion classes closed under …