On prime nearrings with derivations

Abstract

Some results assert that the existence of a suitably constrained derivation on a prime nearring forces the nearring to be ring. The purpose of this paper is to establish some results concerning (α, β)-derivations of prime nearrings. To initiate the study of the theory, the existence of such derivation is shown by an example. Also a posner-type result for the composition of (α, β)-derivation is obtained.

Keywords:

• Derivation
• γ-derivation
• (α, β)-derivation
• Nearring
• Prime nearring