Centralizing Mappings on Semiprime Rings

Abstract

Let R be a semiprime ring, and k be an arbitrary positive integer. We show that R with suitably-restricted additive torsion must contain a nontrivial central ideal if it admits a derivation d which is nonzero on a nontrivial left ideal U of R, and the map d(subscript k-1)(x) is centralizing on U.