ON CONTINUOUS RINGS

We show that if R is a semiperfect ring with essential left socle and rl(K) = K for every small right ideal K of R, then R is right continuo us. Accordingly some well-known classes of rings, such as dual rings a nd rings all of whose cyclic right R-modules are essentially embedded in projectives, are shown to be continuous. We also prove that a ring R has a perfect duality if and only if the dual of every simple right R-module is simple and R + R is 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. (C) 1997 Academic Press .