A ring is called quasi-Frobenius if it is right or left selfinjective, and right or left artinian (all
four combinations are equivalent). The study of these rings grew out of the theory of …

This unique and comprehensive volume provides an up-to-date account of the literature on
the subject of determining the structure of rings over which cyclic modules or proper cyclic …

A ring R is called right weakly continuous if the right annihilator of each element is essential
in a summand of R, and R satisfies the right C2-condition (every right ideal that is isomorphic …

If M and N are right R-modules, M is called Socle-N-injective (Soc-N-injective) if every R-
homomorphism from the socle of N into M extends to N. Equivalently, for every semisimple …

Abstract A right R-module M is virtually extending (or CIS) if every complement submodule of
M is isomorphic to a direct summand of M, and M is called a virtually C2-module if every …

We show that ifRis a semiperfect ring with essential left socle andrl (K)= Kfor every small
right idealKofR, thenRis right continuous. Accordingly some well-known classes of rings …

Let SM R be an (S, R)-bimodule and denote lS (A)= 1 s∈ S: sA= 0l for any submodule A of
MR. Extending the notion of an Ikeda-Nakayama ring, we investigate the condition lS (A n …

It is proved that if every cyclic right R-module is torsionless and R is a left CS-ring then R is
semiperfect left continuous with soc (RR) essential in RR. As a consequence every right …

An interesting property of artinian modules is that they have finitely generated essential
socle. The modules with this property are called finitely embedded or finitely cogenerated …

CS rings and nakayama permutations Page 1 COMMUNICATIONS IN ALGEBRA, 25(12),
3787-3795 (1997) CS RINGS AND NAKAYAMA PERMUTATIONS Mohamed F. Yousif …