The 𝒯-divisible R-modules are defined in terms of a hereditary torsion theory of modules
over an associative ring R with identity element. In the special case where 𝒯 is the usual …

The concept of an h-divisible module over a domain R was introduced by Matlis in [4]; these
modules are by definition the epimorphic images of the injective R-modules. The purpose of …

The aim of this paper is to describe an equivalence between the full subcategory of Mod-R
whose objects are all the divisible modules over an integral domain R and a suitable full …

This note is devoted to the study of divisible modules over arbitrary commutative domains R
with 1. Whereas divisible modules over Dedekind domains can be completely characterized …

Introduction. Let R be an integral domain with quotient field Q, and let A be a module over R.
A is said to be a divisible R-module, if rA= A for every r7OER. An element xEA is said to be a …

In this paper, all rings R have an identity element 1 and all modules are unital left ft-modules
unless it is specifically indicated to the contrary. Additionally, r will always denote a nontrivial …

A classical question for modules over an integral domain is," When is the torsion submodule
t (A) of a module A a direct summand of AT'A module is said to split when its torsion …

Recently, de la Rosa and Fuchs (Commentarii Math. Univ. Sancti Pauli 35 (1986), 53–57)
discussed the relationship between the projective dimen-sion and the ha-dimension of a …

Let (𝒯, ℱ) denote a hereditary torsion theory for the category of modules over a ring R. In this
paper the splitting of projective modules is studied, and it is shown that this is not equivalent …

It is well known that for an integral domain $ A $, the property that a module is divisible if and
only if it is injective is equivalent to the property that $ A $ is a Dedekind domain. In this …