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 char$R > s + t$ or char$R = 0$, 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 char$R > n$ or char$R = 0$, then $R$ is commutative.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2015.03.01}, url = {http://global-sci.org/intro/article_detail/cmr/18921.html} }