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 …

Rings Whose Modules Are {oplus}-Supplemented Page 1 Ž . Journal of Algebra 218, 470487
1999 Article ID jabr.1998.7830, available online at http:rrwww.idealibrary.com on Rings Whose …

A module M is defined to be a CS module, if every submodule of M is essential in a direct
summand of M. In this paper we show, among other results, that for a right nonsingular ring …

A module M is said to satisfy the condition (℘*) if M is a direct sum of a projective module
and a quasi-continuous module. In an earlier paper, we described the structure of rings over …

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 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 …

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 …

R is called a right WV-ring if each simple right R-module is injective relative to proper cyclics.
If R is a right WV-ring, then R is right uniform or a right V-ring. It is shown that a right WV-ring …

Let $ R $ be an artinian ring such that for the Jacobson radical $ J $ of $ R $, $ R/J $ is a
direct product of matrix rings over finite-dimensional division rings. Then the following are …

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 …