Throughout this paper it is assumed that rings are associative, have the identity element,
and all modules are left unital. R will denote a ring with identity, R-Mod the category of left R …

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 …

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 …

Introduction: Let R be a ring with identity. By an R-module we will mean a unitary R-module
which is a left module unless otherwise stated. Let 7 be a hereditary torsion theory. A …

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 …

The purpose of this thesis is to generalize to the torsion-theoretic setting various concepts
and results from the theory of rings and modules. In order to accomplish this we begin with …

1. INTRODUCTION AND PRELI\lINARIES. 0. Goldman [2] introduced the concept of a-
projectivity for an idempotent kernel functor 3 on the category of modules over a ring R. This …

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 …

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 …