A Commutativity Condition for Semiprime Rings with Generalized Skew Derivations

Let R be a semiprime ring of characteristic different from 2, Z(R) its center, Q its right Martindale quotient ring, C its extended centroid, F a generalized skew derivation of R and \(n\ge 1\) a fixed integer such that \(\bigr (F(x)y+F(y)x-[x,y]\bigl )^n=0\) , for all \(x,y \in R\) . Then R is commutative and \(F=0\) .