## On continuous rings.(English)Zbl 0884.16002

From the abstract: 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 continuous. Accordingly some well-known classes of rings, such as dual 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 $$R\oplus R$$ (a direct sum) is a left and right CS module. In Section 2 of the paper we provide a characterization for semiperfect right self-injective rings in terms of the CS-condition.

### MSC:

 16D50 Injective modules, self-injective associative rings 16L30 Noncommutative local and semilocal rings, perfect rings
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### References:

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