N - Commuting Maps on Semiprime Rings

Adil   Naoum; A.   Majeed; Samer   Hassin

doi:10.24996/ijs.2007.48.1.%g

N - Commuting Maps on Semiprime Rings

Authors

Adil Naoum Department of Mathematics, College of Science, University of Baghdad. Baghdad-Iraq.
A. Majeed Department of Mathematics, College of Science, University of Baghdad. Baghdad-Iraq.
Samer Hassin Department of Mathematics, College of Science, University of Baghdad. Baghdad-Iraq.

DOI:

https://doi.org/10.24996/ijs.2007.48.1.%25g

Keywords:

Maps, 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: )R(Z)]x(d,x[xm
i-
n - commuting on U.
ii-
n - skew - commuting on U.