An identity on automorphisms of Lie ideals in prime rings
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 \(R\),...
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| Date: | 2022 |
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| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2022
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1612 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543338558128128 |
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| author | Rehmam, N. |
| author_facet | Rehmam, N. |
| author_sort | Rehmam, N. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2022-10-14T16:01:17Z |
| description | 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 \(R\), whenever \(\operatorname{char}(R)>n+m\) or \(\operatorname{char}(R)=0\), where \(n\) and \(m\) are fixed positive integer. |
| first_indexed | 2026-02-08T07:57:43Z |
| format | Article |
| id | admjournalluguniveduua-article-1612 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:57:43Z |
| publishDate | 2022 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-16122022-10-14T16:01:17Z An identity on automorphisms of Lie ideals in prime rings Rehmam, N. prime ring, automorphisms; maximal right ring of quotients, generalized polynomial identity 16N60, 16W20, 16R50 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 \(R\), whenever \(\operatorname{char}(R)>n+m\) or \(\operatorname{char}(R)=0\), where \(n\) and \(m\) are fixed positive integer. Lugansk National Taras Shevchenko University 2022-10-14 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1612 10.12958/adm1612 Algebra and Discrete Mathematics; Vol 33, No 2 (2022) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1612/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1612/716 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1612/1009 Copyright (c) 2022 Algebra and Discrete Mathematics |
| spellingShingle | prime ring automorphisms; maximal right ring of quotients generalized polynomial identity 16N60 16W20 16R50 Rehmam, N. An identity on automorphisms of Lie ideals in prime rings |
| title | An identity on automorphisms of Lie ideals in prime rings |
| title_full | An identity on automorphisms of Lie ideals in prime rings |
| title_fullStr | An identity on automorphisms of Lie ideals in prime rings |
| title_full_unstemmed | An identity on automorphisms of Lie ideals in prime rings |
| title_short | An identity on automorphisms of Lie ideals in prime rings |
| title_sort | identity on automorphisms of lie ideals in prime rings |
| topic | prime ring automorphisms; maximal right ring of quotients generalized polynomial identity 16N60 16W20 16R50 |
| topic_facet | prime ring automorphisms; maximal right ring of quotients generalized polynomial identity 16N60 16W20 16R50 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1612 |
| work_keys_str_mv | AT rehmamn anidentityonautomorphismsoflieidealsinprimerings AT rehmamn identityonautomorphismsoflieidealsinprimerings |