Injective covers of modules were introduced by Enochs [5] as a categorical dual of an
injective envelope and they have been investigated by many authors. The T-torsionfree …

We study C-covers in the context of Grothendieck categories. Namely, we analyse when a
functor between two Grothendieck categories preserves or reflects C-covers. We apply our …

We study the existence of covers and envelopes by some special functors on the category of
finitely presented modules. As an application, we characterize some important rings using …

Throughout the following, R will always denote a ring with multiplicative identity 1 and all
modules will be taken from the category R--mod of unitary left R-modules. Morphisms in R …

T-torsion-free T-injective covers Page 1 COMMUNICATIONS IN ALGEBRA, 12(21), 2707-2726
(1984) 7-TOXSION-FREE T-INJECTIVE c'i3VERS Blas Torrecillas Jover Departamento de …

Throughout this paper R will be a commutative ring with one, and all R-modules will be
unitary. Our purpose is to study commutative ring exten-sions S of R. As a key tool in our …

Notation and terminology concerning (hereditary) torsion theories on R-mod will follow [I]. In
particular, if T is a torsion theory on R-mod then a left ideal H of R is said to be T-dense in R …

The use of category equivalences for the study of endomorphism rings stems from the Morita
theorem. In a sense, this theorem can be viewed as stating that if P is a finitely generated …

INTRODUCTION A ring R is called a left V-ring if every simple left R-module is injective. In
this paper, we study V-rings relative to left Gabriel topologies on R. Our initial motivation is …

It is well known that over a left Notherian ring any direct sum of injecive modules is again
injective, and every injective module is a direct sum of indecomposable modules. Faith [6] …