Author/Authors :
Naoum, Adil G. University of Baghdad - College of Science - Department of Mathematics, Iraq , Majeed, A. H. University of Baghdad - College of Science - Department of Mathematics, Iraq , Hassin, Samer K. University of Baghdad - College of Science - Department of Mathematics, Iraq
Abstract :
Let R be a ring with center Z (R) , 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 x →[x^m،d(x)] satisfies one of the following: i- n - commuting on U. ii- n - skew - commuting on U
