Abstract
In the present paper, we prove that a prime ring R with center Z satisfies s(4), the standard identity in four variables if R admits a non-identity automorphism sigma such that ([u(sigma); u]v(sigma) + v(sigma)[u(sigma); u])(n) is an element of Z for all u, v in some non-central Lie ideal L of R whenever either char(R) > n or char(R) = 0, where n is a fixed positive integer. (C) 2018 Mathematical Institute Slovak Academy of Sciences