Derivations of higher order in semiprime rings

Abstract

Let R be a 2-torsion free semiprime ring with derivation d. Supposed d2n is a derivation of R, where n is a positive integer. It is shown that if R is (4n−2)-torsion free or if R is an inner derivation of R, then d2n−1=0.

Keywords

• Derivation
• semiprime ring
• nilpotent derivation.