Some commutativity criteria for prime rings with involution involving symmetric and skew symmetric elements
UDC 512.5 We study the Posner second theorem [Proc. Amer. Math. Soc., 8, 1093–1100 (1957)] and strong com\-mu\-ta\-tivity preserving problem for symmetric and skew symmetric elements involving generalized derivations on prime rings with involution. The obtained results cover numer...
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| Date: | 2023 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2023
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/6751 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512505933070336 |
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| author | Dar, N. A. Ali, S. Abbasi, A. Ayedh, M. Dar, N. A. Ali, S. Abbasi, A. Ayedh, M. |
| author_facet | Dar, N. A. Ali, S. Abbasi, A. Ayedh, M. Dar, N. A. Ali, S. Abbasi, A. Ayedh, M. |
| author_sort | Dar, N. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2023-05-14T15:30:07Z |
| description |
UDC 512.5
We study the Posner second theorem [Proc. Amer. Math. Soc., 8, 1093–1100 (1957)] and strong com\-mu\-ta\-tivity preserving problem for symmetric and skew symmetric elements involving generalized derivations on prime rings with involution. The obtained results cover numerous known theorems. We also provide examples showing that the obtained results hold neither in the case of involution of the first kind, nor in the case where the ring is not prime. |
| doi_str_mv | 10.37863/umzh.v75i4.6751 |
| first_indexed | 2026-03-24T03:29:52Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-6751 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:29:52Z |
| publishDate | 2023 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-67512023-05-14T15:30:07Z Some commutativity criteria for prime rings with involution involving symmetric and skew symmetric elements Some commutativity criteria for prime rings with involution involving symmetric and skew symmetric elements Dar, N. A. Ali, S. Abbasi, A. Ayedh, M. Dar, N. A. Ali, S. Abbasi, A. Ayedh, M. Generalized derivation, involution, prime ring, symmetric and skew symmetric element Algebra(Ring Theory) UDC 512.5 We study the Posner second theorem [Proc. Amer. Math. Soc., 8, 1093–1100 (1957)] and strong com\-mu\-ta\-tivity preserving problem for symmetric and skew symmetric elements involving generalized derivations on prime rings with involution. The obtained results cover numerous known theorems. We also provide examples showing that the obtained results hold neither in the case of involution of the first kind, nor in the case where the ring is not prime. УДК 512.5  Деякі критерії комутативності простих кілець з інволюцією симетричних та кососиметричних елементів  Вивчається друга теорема Познера [Proc. Amer. Math. Soc., 8, 1093–1100 (1957)] та проблема збереження сильної комутативності для симетричних і кососиметричних елементів, що включає узагальнені похідні на простих кільцях з інволюцією. Отримані результати охоплюють багато відомих теорем. Крім того, наведено приклади, які показують, що отримані результати несправедливі ні у випадку інволюції першого роду, ні у випадку, коли кільце не є простим. Institute of Mathematics, NAS of Ukraine 2023-05-10 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/6751 10.37863/umzh.v75i4.6751 Ukrains’kyi Matematychnyi Zhurnal; Vol. 75 No. 4 (2023); 455 - 466 Український математичний журнал; Том 75 № 4 (2023); 455 - 466 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/6751/9779 Copyright (c) 2023 Nadeem Ahmad Dar, SHAKIR ALI, Adnan Abbasi, Mohammad Ayedh |
| spellingShingle | Dar, N. A. Ali, S. Abbasi, A. Ayedh, M. Dar, N. A. Ali, S. Abbasi, A. Ayedh, M. Some commutativity criteria for prime rings with involution involving symmetric and skew symmetric elements |
| title | Some commutativity criteria for prime rings with involution involving symmetric and skew symmetric elements |
| title_alt | Some commutativity criteria for prime rings with involution involving symmetric and skew symmetric elements |
| title_full | Some commutativity criteria for prime rings with involution involving symmetric and skew symmetric elements |
| title_fullStr | Some commutativity criteria for prime rings with involution involving symmetric and skew symmetric elements |
| title_full_unstemmed | Some commutativity criteria for prime rings with involution involving symmetric and skew symmetric elements |
| title_short | Some commutativity criteria for prime rings with involution involving symmetric and skew symmetric elements |
| title_sort | some commutativity criteria for prime rings with involution involving symmetric and skew symmetric elements |
| topic_facet | Generalized derivation involution prime ring symmetric and skew symmetric element Algebra(Ring Theory) |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/6751 |
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