Some Results On Lie Ideals With (σ,τ)-derivation In Prime Rings

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 subset of Z(R) (or aU subset of Z(R)) for a element of R, then either or U is commutative Also, we assumed that Uis a ring to prove that: (i) If Ua subset of Z(R) (or aU subset of Z(R)) for a element of R, then either a=0 or U is commutative. (ii) If ad(U)=0 (or d (U)a=0) for a element of R, then either a=0 or U is commutative. (iii) If d is a homomorphism on U such that ad(U) subset of Z(R)(or d(U)a subset of Z(R), then a=0 or U is commutative.