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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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