For an arbitrary, abstract class L of right R-modules, various characterisations of L-injectivity
are given assuming various natural conditions on L. We investigate what the minimum …

Let R be a ring and M a right R-module. Several authors have considered when the module
M has the property that all modules in a specified class are M-injective. For example, Hirano …

Throughout all rings R are associative wit, h identity, and all modules are unitary right R-
modules. Mod-R will denote the category of unitary right R-modulcs. A classical result in ring …

Let R be an associative ring with 1 and let T be a hereditary torsion theory in the category of
left R-modules. In defining the localizatio n of R respect to x, the concept of T-injective …

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 …

In the previous paper [g] we have introduced the notion of a cyclic-hereditary torsion class
for the category mod-R of unital right R-modules over a ring R with unit as a torsion class …

Let τ be a hereditary torsion theory. We mention a characterization of τ-quasi-injective
modules, as fully invariant submodules of their τ-injective hull, and we give some properties …

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 …

Throughout this paper R is a ring with identity and every i?-module is unital. Let r be a
hereditary torsion theory with respect to R (see Golan [3]). A submodule N of a right i …

Introduction. In this paper, we will prove some results on chain conditions of modules with
respect to an 1ll-natural class, extending several well-known theorems of Golan [5], Miller …