Let M1,…, Mn be right modules over a ring R. Suppose that the endomorphism ring EndR
(Mi) of each module Mi has at most two maximal right ideals. Is it true that every direct …

For a ring R, there are classical facts that R is right Noetherian if and only if every direct sum
of injective right R-modules is injective, and R is right Noetherian if and only if every …

Let R be an associative ring with identity. We show that every direct sum of singular injective
right R-modules is injective iff any one of the following equivalent conditions holds. i) Every …

ABSTRACT A principal right ideal of a ring is called uniquely generated if any two elements
of the ring that generate the same principal right ideal must be right associated (ie, if for all a …

In this note, we study rings over which every left module is a direct sum of finitely generated
modules. Chase [5] showed that all such rings are left artinian and Fuller [8] proved that …

We show that the indecomposable R-modules whose endomorphism ring has finitely many
maximal right ideals, all of them two-sided, have a surprisingly simple behavior as far as …

It is known that every essential extension of a direct sum of injective hulls of simple R-
modules is a direct sum of injective R-modules if and only if the ring R is right noetherian …

It is shown that every pure-injective right module over a ring R is a direct sum of lifting
modules if and only if R is a ring of finite representation type and right local type. In …

In this paper, we provide several new characterizations of the maximal right ring of quotients
of a ring by using the relatively dense property. As a ring is embedded in its maximal right …

Let R be a ring with identity. A unital left R-module M has the min-property provided the
simple submodules of M are independent. On the other hand a left R-module M has the …