On Additivity and Multiplicativity of Centrally Extended α,β-Higher Derivations in Rings

Abstract

In this paper, the concept of centrally extended α,β-higher derivations is studied. It is shown to be additive in a ring without nonzero central ideals. Also, we prove that in semiprime rings with no nonzero central ideals, every centrally extended α,β-higher derivation is an α,β-higher derivation. Some examples are given to show that our theorems’ assumptions cannot be relaxed. The invariance problem of the center of the ring is also investigated.