Some results on lie ideals with (σ,τ)‎-derivation in prime rings

Abstract EN

In this paper, we proved that if R is a prime ring, U be a nonzero Lie ideal of R , d be a nonzero (σ,τ)-derivation of R.

Then if UaZ(R) (or aUZ(R)) for aR, then either or U is commutative Also, we assumed that Uis a ring to prove that: (i) If UaZ(R) (or aUZ(R)) for aR, then either a=0 or U is commutative.

(ii) If ad(U)=0 (or d(U)a=0) for aR, then either a=0 or U is commutative.

(iii) If d is a homomorphism on U such that ad(U) Z(R)(or d(U)aZ(R), then a=0 or U is commutative.