On Herstein's identity in prime rings

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 \(\...

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Bibliographic Details
Date:2022
Main Author: Sandhu, G. S.
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2022
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Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1581
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics