Abstract :
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, such as dual rings and rings all of whose cyclic rightR-modules are essentially embedded in projectives, are shown to be continuous. We also prove that a ringRhas a perfect duality if and only if the dual of every simple rightR-module is simple andR circled plus Ris a left and right CS-module. In Sect. 2 of the paper we provide a characterization for semiperfect right self-injective rings in terms of the CS-condition.
