N-commuting maps on semiprime rings

الملخص EN

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.