Abstract
For a ring R with an automorphism alpha an n-additive mapping D : R-n -> R is called a skew n-derivation w.r.t. alpha if it is an alpha-derivation of R for each argument. Namely it is always an alpha-derivation of R for the argument being left once (n - 1) arguments are fixed by (n - 1) elements in R. In the present note, begin with a result of Park [9], we prove that if a skew n-derivation D associated with an automorphism alpha with trace tau of a noncommutative n! torsion free semiprime ring R satisfying [tau(x),alpha(x)] is an element of Z(R) for all x is an element of I, then [tau(x),alpha(x)] = 0 for all x is an element of I, a nonzero ideal of R. Moreover, we investigate the commutativity in case of prime rings.