Let $ R $ be a subring of the rationals. We want to investigate self splitting $ R $-modules $
G $(that is $\operatorname {Ext} _R (G, G)= 0) $. Following Schultz, we call such modules …

Let R be a ring and let t be a torsion preradical, R is said to have the splitting property,
provided that for every left R-module M, the torsion submodule t (M) of M is a direct …

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 …

In this note we characterize those torsion theories over a semiperfect ring such that the class
of torsion free modules is closed under projective covers and the hereditary torsion theories …

Let R be a ring, M a right R-module, and na fixed non-negative integer. M is called n-
cotorsion if for any flat right R-module N. M is said to be n-flat if for any n-cotorsion right R …

The purpose of this paper is to introduce the study of perfect torsion theories on
$\operatorname {Mod} R $ and to dualize the concept of divisible module. A torsion theory …

We introduce the notion of a duality pair and demonstrate how the left half of such a pair is"
often" covering and preenveloping. As an application, we generalize a result by Enochs et …

We generalize Hill's lemma in order to obtain a large family of C-filtered submodules from a
single C-filtration of a module. We use this to prove the following generalization of …

An additive functor from the category of flat right R‐modules to the category of abelian
groups is continuous if it is isomorphic to a functor of the form−⊗ RM, where M is a left R …

It is proved that a ring R is right perfect if and only if it is Σ-cotorsion as a right module over
itself. Several other conditions are shown to be equivalent. For example, that every pure …