Year: 2015
Author: Shuliang Huang
Communications in Mathematical Research , Vol. 31 (2015), Iss. 3 : pp. 193–198
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.13447/j.1674-5647.2015.03.01
Communications in Mathematical Research , Vol. 31 (2015), Iss. 3 : pp. 193–198
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 6
Keywords: prime ring Lie ideal automorphism.