RIGHT (σ,τ)-DERIVATIONS ON LEFT IDEALS

Abstract

Let R be a prime ring and I a nonzero left Ideal of R which is a semi prime as a ring.
For a right (σ,τ) – derivations δ:R → R, we prove the following results:
(1) If δ acts as a homomorphism on I, then δ= 0 on R.
(2) If δ acts as an anti- homomorphism on I, then either δ = 0 on R or I  Z(R).