HIGHER LEFT DERIVATIONS ON SEMIPRIME RINGS

In this note, we extend the Bregar and Vukman's result [1, Proposition 1.6], which is well-known, to higher left derivations as follows: let R be a ring. (i) Under a certain condition, the existence of a nonzero higher left derivation implies that R is commutative. (ii) if R is semiprime, every higher left derivation on R is a higher derivation which maps R into its center.