Centralizing n-Homoderivations of Semiprime Rings

Abstract

We introduce the notion of n-homoderivation on a ring ℜ and show that a semiprime ring ℜ must have a nontrivial central ideal if it admits an appropriate n-homoderivation which is centralizing on some nontrivial one-sided ideal. Under similar hypotheses, we prove commutativity in prime rings.