On symmetric bi-derivations acting upon prime ideals in any rings
UDC 512.5 Let $R$ be a ring, $P$ be a prime ideal of $R$, $I$ be a nonzero ideal of $R$ such that $P\subsetneq I$, $D_{1}, D_{2}, D_{3}\colon R\times R\rightarrow R$ be symmetric bi-derivations, and $d_{1},\ d_{2},$ and $d_{3}$ be the traces of $D_{1},D_{2},$ and $D_{3}$ respectively. We study the...
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| Дата: | 2026 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
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Institute of Mathematics, NAS of Ukraine
2026
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/9223 |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513451709825024 |
|---|---|
| author | Sögütcü, Emine Koç Gölbaşı, Öznur Dhara, Basudeb Sögütcü, Emine Koç Gölbaşı, Öznur Dhara, Basudeb |
| author_facet | Sögütcü, Emine Koç Gölbaşı, Öznur Dhara, Basudeb Sögütcü, Emine Koç Gölbaşı, Öznur Dhara, Basudeb |
| author_sort | Sögütcü, Emine Koç |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-03-21T13:35:35Z |
| description | UDC 512.5
Let $R$ be a ring, $P$ be a prime ideal of $R$, $I$ be a nonzero ideal of $R$ such that $P\subsetneq I$, $D_{1}, D_{2}, D_{3}\colon R\times R\rightarrow R$ be symmetric bi-derivations, and $d_{1},\ d_{2},$ and $d_{3}$ be the traces of $D_{1},D_{2},$ and $D_{3}$ respectively. We study the following conditions: (i) $[d_1(x),x]\in P,$ (ii) $d_1(x)\circ x\in P,$ (iii) $D_{1}(d_{2}(x),x)\in P,$ (iv) $d_{1}(d_{2}(x))\pm d_{3}(x)\in P,$ and (v) $d_{1}(x)d_{2}(x)\in P$ for all $x,y\in I.$ |
| doi_str_mv | 10.3842/umzh.v77i11.9223 |
| first_indexed | 2026-03-24T03:44:54Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-9223 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:44:54Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-92232026-03-21T13:35:35Z On symmetric bi-derivations acting upon prime ideals in any rings On symmetric bi-derivations acting upon prime ideals in any rings Sögütcü, Emine Koç Gölbaşı, Öznur Dhara, Basudeb Sögütcü, Emine Koç Gölbaşı, Öznur Dhara, Basudeb Prime rings prime ideals derivations bi-derivations Keywords and Phrases: Prime rings, prime ideals, derivations, bi-derivations Mathematics Subject Classification: 16W25, 16W10, 16U80 UDC 512.5 Let $R$ be a ring, $P$ be a prime ideal of $R$, $I$ be a nonzero ideal of $R$ such that $P\subsetneq I$, $D_{1}, D_{2}, D_{3}\colon R\times R\rightarrow R$ be symmetric bi-derivations, and $d_{1},\ d_{2},$ and $d_{3}$ be the traces of $D_{1},D_{2},$ and $D_{3}$ respectively. We study the following conditions: (i) $[d_1(x),x]\in P,$ (ii) $d_1(x)\circ x\in P,$ (iii) $D_{1}(d_{2}(x),x)\in P,$ (iv) $d_{1}(d_{2}(x))\pm d_{3}(x)\in P,$ and (v) $d_{1}(x)d_{2}(x)\in P$ for all $x,y\in I.$ УДК 512.5 Про симетричні білінійні похідні, що діють на прості ідеали в будь-яких кільцях Нехай $R$ – кільце, $P$ – простий ідеал кільця $R$, $I$ – ненульовий ідеал кільця $R$ такий, що $P\subsetneq I$, $D_{1}, D_{2},\ D_{3}\colon R\times R\rightarrow R$ – симетричні білінійні похідні, а $d_{1},\ d_{2},\ d_{3}$ – відповідно їхні сліди. У статті розглянуто такі умови для всіх $x,y\in I$: (i) $[d_1(x),x]\in P,$ (ii) $d_1(x)\circ x\in P,$ (iii) $D_{1}(d_{2}(x),x)\in P,$ (iv) $d_{1}(d_{2}(x))\pm d_{3}(x)\in P,$ (v) $d_{1}(x)d_{2}(x)\in P.$ Institute of Mathematics, NAS of Ukraine 2026-03-21 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/9223 10.3842/umzh.v77i11.9223 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 11 (2025); 696 Український математичний журнал; Том 77 № 11 (2025); 696 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/9223/10601 Copyright (c) 2025 Emine Koç Sögütcü, Öznur Gölbaşı, Basudeb Dhara |
| spellingShingle | Sögütcü, Emine Koç Gölbaşı, Öznur Dhara, Basudeb Sögütcü, Emine Koç Gölbaşı, Öznur Dhara, Basudeb On symmetric bi-derivations acting upon prime ideals in any rings |
| title | On symmetric bi-derivations acting upon prime ideals in any rings |
| title_alt | On symmetric bi-derivations acting upon prime ideals in any rings |
| title_full | On symmetric bi-derivations acting upon prime ideals in any rings |
| title_fullStr | On symmetric bi-derivations acting upon prime ideals in any rings |
| title_full_unstemmed | On symmetric bi-derivations acting upon prime ideals in any rings |
| title_short | On symmetric bi-derivations acting upon prime ideals in any rings |
| title_sort | on symmetric bi-derivations acting upon prime ideals in any rings |
| topic_facet | Prime rings prime ideals derivations bi-derivations Keywords and Phrases: Prime rings prime ideals derivations bi-derivations Mathematics Subject Classification: 16W25 16W10 16U80 |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9223 |
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