N-Commuting skew higher derivation on semiprime rings

Abstract

In this article we study skew higher derivation (d_i)_{i\in \mathbb{N}} on semiprime ring R with suitable torsion restriction and we prove that every n-centralizing skew higher derivation is n-commuting. Further, we show that if a ring R has n-centralizing skew higher derivation then either R is commutative or some linear combination of (d_i)_{i\in \mathbb{N}} maps center of R to zero.