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 \(\...
Gespeichert in:
| Datum: | 2022 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2022
|
| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1581 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| _version_ | 1856543240241545216 |
|---|---|
| author | Sandhu, G. S. |
| author_facet | Sandhu, G. S. |
| author_sort | Sandhu, G. S. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2022-06-15T04:49:44Z |
| 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. |
| first_indexed | 2025-12-02T15:30:25Z |
| format | Article |
| id | admjournalluguniveduua-article-1581 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:30:25Z |
| publishDate | 2022 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-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 |
| spellingShingle | prime rings lie ideal generalized derivation automorphism GPIs 16W10 16N60 16W25 Sandhu, G. S. On Herstein's identity in prime rings |
| title | 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_short | On Herstein's identity in prime rings |
| title_sort | on herstein's identity in prime rings |
| topic | prime rings lie ideal generalized derivation automorphism GPIs 16W10 16N60 16W25 |
| topic_facet | prime rings lie ideal generalized derivation automorphism GPIs 16W10 16N60 16W25 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1581 |
| work_keys_str_mv | AT sandhugs onhersteinsidentityinprimerings |