91. Background A subclass T of mod-R is called an hereditary torsion class if it is closed
under submodul es, homomorphic images, extensions and direct sums. The class T …

JP Jans has shown that if a ring R is right perfect, then a certain torsion in the category Mod
R of left R-modules is closed under taking direct products. Extending his method, JS Alin …

Let R be a ring and let R-mod denote the category of all left R-modules. If T is a (hereditary)
torsion theory on R-mod then a left R-module M is said to have a T-composition series if and …

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 …

Let R be a small preadditive category, viewed as a “ring with several objects.” A right R-
module is an additive functor from Rop to the category Ab of abelian groups. We show that …

A well-known theorem of Hopkins and Levitzki states that any left artinian ring with identity
element is left noetherian. The main theorem of this paper generalizes this to the situation of …

Recently, Rim and Teply, using the notion of $\tau $-exact modules, found a necessary
condition for the existence of $\tau $-torsionfree covers with respect to a given hereditary …

In this paper divisible and codivisible modules are studied relative to a torsion theory on
Mod. fi. It is shown, for example, that if the tor sion theory is hereditary, then the following are …

Let Rbe a ring with identity. Chase [5] has characterized the right coherent rings; he has
shown that arbitrary products of RR are flat if and only if finitely generated submodules of …