N - Commuting Maps on Semiprime Rings

Abstract

Let R be a ring with center , and n, m are arbitrary positive integers. We show that a semiprime ring R with suitable - restriction must contain a nonzero central ideal, if it admits a derivation d which is nonzero on a non trivial left ideal U of R and the map satisfies one of the following:
i-n - commuting on U.
ii-n - skew - commuting on U.