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Abstract Let R be a ring with center Z, and S a nonempty subset of R . A mapping F from R to R is called centralizing on S if x, F(x) ∊ Z for all x ∊ S . We show that a semiprime ring R must have a nontrivial central ideal if it admits an appropriate endomorphism or derivation which is centralizing on some nontrivial one-sided ideal. Under similar hypotheses, we prove commutativity in prime rings.
Bell et al. (Sun,) studied this question.