ON RIGHT GENERALIZED (α,β)-DERIVATIONS IN PRIME RINGS

Abstract

Breˇ sar proved that the only semiderivations of prime rings are derivations and mappings of the form D(x)=λ(x−α(x)), where α is an endomorphism and λ is an element in the extended centroid. De Filippis, Mamouni and Oukhtite extended this result to generalized semiderivations. The aim of this note is to extend their results to right generaliged (α,β)-derivations with reduction of some conditions, where α is an epimorphism and β is an endomorphism