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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| Дата: | 2022 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2022
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1581 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-15812022-06-15T04:49:44Z On Herstein's identity in prime rings Sandhu, G. S. prime rings, lie ideal, generalized derivation, automorphism, GPIs 16W10, 16N60, 16W25 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 \(\sigma([x,y])^{n}=\sigma([x,y]),\) where \(F\) and \(\sigma\) are generalized derivation and automorphism of a prime ring \(R\), respectively and \(n>1\) a fixed integer. Lugansk National Taras Shevchenko University 2022-06-15 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1581 10.12958/adm1581 Algebra and Discrete Mathematics; Vol 33, No 1 (2022) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1581/pdf Copyright (c) 2022 Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics |
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| datestamp_date |
2022-06-15T04:49:44Z |
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OJS |
| language |
English |
| topic |
prime rings lie ideal generalized derivation automorphism GPIs 16W10 16N60 16W25 |
| spellingShingle |
prime rings lie ideal generalized derivation automorphism GPIs 16W10 16N60 16W25 Sandhu, G. S. On Herstein's identity in prime rings |
| topic_facet |
prime rings lie ideal generalized derivation automorphism GPIs 16W10 16N60 16W25 |
| format |
Article |
| author |
Sandhu, G. S. |
| author_facet |
Sandhu, G. S. |
| author_sort |
Sandhu, G. S. |
| title |
On Herstein's identity in prime rings |
| title_short |
On Herstein's identity in prime rings |
| title_full |
On Herstein's identity in prime rings |
| title_fullStr |
On Herstein's identity in prime rings |
| title_full_unstemmed |
On Herstein's identity in prime rings |
| title_sort |
on herstein's identity in prime rings |
| description |
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 \(\sigma([x,y])^{n}=\sigma([x,y]),\) where \(F\) and \(\sigma\) are generalized derivation and automorphism of a prime ring \(R\), respectively and \(n>1\) a fixed integer. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2022 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1581 |
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AT sandhugs onhersteinsidentityinprimerings |
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2025-07-17T10:32:25Z |
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2025-07-17T10:32:25Z |
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