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 …

For a hereditary torsion theory T, this paper mainly discuss properties of A-τ-injective
modules, where A is a fixed left R-module. It is proved that if M is an A-τ-injective, B is a …

In this paper, we introduce and study torsion-theoretic generalizations of singular and
nonsingular modules by using the concept of τ-essential submodule for a hereditary torsion …

Let $\tau $ be a given hereditary torsion theory for left R-module category R-Mod. The class
of all $\tau $-torsion left R-modules, denoted by T is closed under homomorphic images …

In this paper, we give some characterizations of modules M over a ring R such that every
submodule has a unique closure relative to a hereditary torsion theory on Mod-R by using …

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 …

Injective and projective modules are studied relative to a hereditary torsion theory τ on Mod–
R. It is shown that every τ–projective module is projective if and only if the torsion ideal of R …

An R-module M is said to be a C1-module if every closed submodule of M is a direct
summand. In this paper we introduce and investigate the concept of the\tau-C1 module for a …

Let τ be a hereditary torsion theory. The purpose of this paper is to extend results about
singular (resp. nonsingular) modules to τ-singular (resp. τ-nonsigular) modules. An R …

In a previous paper we introduced μ-complemented modules for any given torsion functor μ
of a hereditary torsion theory in Mod-R and presented their basic properties. Our current …