Volume 31, Issue 3
Notes on Automorphisms of Prime Rings

Commun. Math. Res., 31 (2015), pp. 193-198.

Published online: 2021-05

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• 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.

• Keywords

prime ring, Lie ideal, automorphism.

16N60, 16U80, 16W25

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• TXT
@Article{CMR-31-193, author = {Shuliang and Huang and and 19464 and and Shuliang Huang}, title = {Notes on Automorphisms of Prime Rings}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {31}, number = {3}, pages = {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.

}, 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} }
TY - JOUR T1 - Notes on Automorphisms of Prime Rings AU - Huang , Shuliang JO - Communications in Mathematical Research VL - 3 SP - 193 EP - 198 PY - 2021 DA - 2021/05 SN - 31 DO - http://doi.org/10.13447/j.1674-5647.2015.03.01 UR - https://global-sci.org/intro/article_detail/cmr/18921.html KW - prime ring, Lie ideal, automorphism. AB -

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.

Shuliang Huang. (2021). Notes on Automorphisms of Prime Rings. Communications in Mathematical Research . 31 (3). 193-198. doi:10.13447/j.1674-5647.2015.03.01
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