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 …

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 …

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 …

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 …

Throughout this paper we assume that R is a right perfect ring with identity and let Mod-R be
the category of right R-modules. Let M be a right R-module. We denote by 0→ K (M)→ P …

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 and Abstract. It is well known that hereditary torsion theories have been
extensively studied and have much application to ring theoies. Every hereditary torsion …

In this note we characterize those torsion theories over a semiperfect ring such that the class
of torsion free modules is closed under projective covers and the hereditary torsion theories …

Let R be any ring. We prove that every right R-module is coretractable if and only if R is right
perfect and every right R-module is small coretractable if and only if all torsion theories on R …

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 …