An identity on automorphisms of Lie ideals in prime rings

In the present paper it is shown that a prime ring R with center Z satisfies s4, the standard identity in four variables if R admits a non-identity automorphism σ such that [uσ, u] n u σ∈ Z for all u in some non-central Lie ideal L of R, whenever char(R) > n or char(R) = 0 , where n is a fixed positive integer. This result is in the spirit of theorems such as Posner’s second theorem or the Herstein’s theorem on derivations with central values. © 2016, Università degli Studi di Ferrara.