Abstract
An l.p.p. ring satisfying the primitive idempotent condition is called left *-semisimple if it also satisfies the ascending condition on right *ideals. We prove that a left *-semisimple ring can be uniquely decomposed into a direct product of a finite number of full matrix rings over certain domains, up to isomorphism. In fact, such left *-semisimple rings are generalized semisimple rings and, in particular, they are semisimple when they are finite. Mathematics Subject Classification: 16W60
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