(untitled) (Communications in Mathematical Research, 2021)
Let R be a prime ring, L a noncentral Lie ideal and σ a nontrivial automorphism of R such that u^sσ(u)u^t = 0 for all u ∈ L, where s, t are fixed non-negative integers. If either charR > s + t or charR = 0, then R satisfies s_4, the standard identity in four variables. We also examine the identity (σ([x, y])−[x, y])^n = 0 for all x, y ∈ I, where I is a nonzero ideal of R and n is a fixed positive integer. If either charR > n or charR = 0, then R is commutative.