An identity on automorphisms of Lie ideals in prime rings

• Date: 2022
• Main Author: Rehmam, N.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2022
• Subjects: prime ring; automorphisms; maximal right ring of quotients; generalized polynomial identity; 16N60; 16W20; 16R50
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1612
• Journal Title: Algebra and Discrete Mathematics

In the present paper it is shown 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 \( [u, v] - u^{m}[u^\sigma,u]^nu^\sigma\in Z\) for all \(u\) in some noncentral ideal \(L\) of \(R\),...