On Herstein's identity in prime rings

• Date: 2022
• Main Author: Sandhu, G. S.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2022
• Subjects: prime rings; lie ideal; generalized derivation; automorphism; GPIs; 16W10; 16N60; 16W25
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1581
• Journal Title: Algebra and Discrete Mathematics

A celebrated result of Herstein [10, Theorem 6] states that a ring \(R\) must be commutative if \([x,y]^{n(x,y)}=[x,y]\) for all \(x,y\in R,\) where \(n(x,y)>1\) is an integer. In this paper, we investigate the structure of a prime ring satisfies the identity \(F([x,y])^{n}=F([x,y])\) and \(\...