Comparison of Jordan (sigma,tau)- Derivations and Jordan Triple (sigma,tau)- Derivations in Semiprime Rings

Abstract

Let R be a 3!-torsion free semiprime ring, , two endomorphisms of R, : → be an additive mapping and L be a noncentral square-closed Lie ideal of R. An additive mapping : → is said to be a Jordan ( , ) −derivation if ( ²) = ( ) ( ) + ( ) ( ) holds for all , ∈ . Also, d is called a Jordan triple ( , ) −derivation if ( ) = ( ) ( ) + ( ) ( ) ( ) + ( ) ( ), for all , ∈ . In this paper, we proved the following result: d is a Jordan ( , ) −derivation on L if and only if d is a Jordan triple ( , ) −derivation on L.