Centralizing n -Homoderivations of Semiprime Rings

Abstract

We introduce the notion of $n$ -homoderivation on a ring $\Re$ and show that a semiprime ring $\Re$ 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.