Has A Jordan?-derivative On An Idempotent Algebra

In this paper,we shall discuss Jordan ?-derivation of algebras with idempotents.Let ? be an algebra with nontrivial idempotents.Our main result is that under certain conditions every Jordan ?-derivation ? of ? can be expressed as ?=d+?,where d is a ?-derivation and ? is a singular Jordan ?-derivation.This result generalizes Benkovic's result on Jordan ?-derivations of triangular algebras.As an application we shall obtain a description of Jordan ?-derivations of full matrix algebras.