Has A Jordanσ-derivative On An Idempotent Algebra

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