On right (σ,τ)‎- derivation of prime rings

Abstract EN

Let R be a prime ring and δ a right (σ,τ)-derivation on R.

In the present paper we will prove the following results : First, suppose that R is a prime ring and I a non-zero ideal of R if δ acts as a homomorphism on I then δ = 0 on R, and if δ acts an anti- homomorphism on I then either δ=0 on R or R is commutative.

Second, suppose that R is 2-torsion-free prime ring and J a non-zero Jordan ideal and a subring of R, if δ acts as a homomorphism on J then δ = 0 on J, and if δ acts an anti- homomorphism on J then either δ = 0 on J or J Z (R).