On the Periodic Radical of a Ring

Abstract

AbstractLet R be a ring and P(R) the sum of all periodic ideals of R. We prove that P(R) is the intersection of all prime ideals Pα such that contains no nontrivial periodic ideals. We also prove that P(R) = 0 if and only if Rs is a subdirect product of prime rings Rα with P(Rα) = 0.