SOME RESULTS ON GENERALIZED DERIVATIONS AND (σ,τ)-LIE IDEALS

Abstract

Let R be a prime ring with characteristic not 2 and σ,τ,α,β,λ,μ,γ automorphisms of R.Let h:R→R be a nonzero left(resp.right)-generalized (α,β)-derivation, b∈R. and V≠0 a left (σ,τ)-Lie ideal of R.

The main object in this article is to study the situations.

(1) h(I)⊂C_{λ,μ}(V),

(2) bh(I)⊂C_{λ,μ}(V) or h(I)b⊂C_{λ,μ}(V), 

(3) hλ(V)=0, (4) hλ(V)b=0 or bhλ(V)=0.