An identity on automorphisms of Lie ideals in prime rings

Abstract

In the present paper it is shown that a prime ring R with center Z satisfies s4, the standard identity in fourvariables if R admits a non-identity automorphismσsuch that [u, v]−um[uσ,u]nuσ∈Z for all u in some noncentral ideal L of R, whenever char (R)>n+m or char(R)=0, where n and m are fixed positive integer.