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

Abstract

Breˇsar proved that the only semiderivations of prime rings are deriva

tions and mappings of the form D(x) = λ(x − α(x)), where α is an en

domorphism and λ is an element in the extended centroid. De Filippis,

Mamouni and Oukhtite extended this result to generalized semideriva

tions. 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 epi

morphism and β is an endomorphism