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 …

In § 1, we begin with a basic theorem which describes a convenient embedding of a
nonsingular left R-module into a complete direct product of copies of the left injective hull of …

In [2 1, Fuchs has shown that R is a test module for quasiinjective modules. He showed that
if M is a right R-module, M is quasi-injective if and only if for each right ideal K of R, every R …

Generalisations of von Neumann regular rings are considered through annihilators, purity
and certain special cyclic modules. Left self-injective regular, strongly regular and biregular …

In a celebrated theorem, AW Goldie determined necessary and sufficient conditions that a
ring have a left quotient ring which is semisimple with minimum condition [4]. Our first main …

1. Introduction. Let R be a ring (associative and with identity). It is easy to see that every left
ideal of R is the (left) annihilator of a finite subset of R if and only if every cyclic left R-module …

Introduction. Let A be a finite-dimensional algebra with identity element over a field O. Let M
be a finitely generated left A-module. Then M, when regarded as a left representation space …

1. Introduction. As is well known, any two faithful modules over a simple ring are isomorphic
if their endomorphism rings are isomorphic. This theorem, however, cannot be extended to …

An useful tool in the study of the endomorphism ring S of a quasi-injective left R-module U is
the duality defined by RUS which has been recently investigated in several papers ([7],[15]) …

Let A be an associative ring which possesses a unit element t and. satisfies the minimum
condition for left ideals. Recently NAGAO-NAKAYA~ IA [9] have determined the structure of …