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 …

We prove that for a ring $ R $, the following are equivalent:(i) Every right $ R $-module is a
direct sum of extending modules, and (ii) $ R $ has finite type and right colocal type (ie …

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 …

One of the fundamental problems in the theory of rings is to characterize the rings of
bounded representations type in terms of their structure. The problem has been solved for …

A right $ R $-module $ M $ is called $ R $-projective provided that it is projective relative to
the right $ R $-module $ R_ {R} $. This paper deals with the rings whose all nonsingular …

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 …

Necessary and sufficient conditions on a ring R are found under which all surjective
endomorphisms of finitely generated right R-modules are automorphisms. Namely, this …

A module M over a ring is called simple-direct-injective if, whenever A and B are simple
submodules of M with A≅ B and B⊆⊕ M, we have A⊆⊕ M. Various basic properties of …

Every indecomposable module over a generalized uniserial ring is uniserial, hence local.
This motivates one to study rings R satisfying the condition (*): R is a right artinian ring such …

A unitary left R-module M over a left noetherian ring R with identity is called admissible if
every prime ideal of R, which is the left annihilator of all nonzero submodules of a …