$S$-weakly prime ideals in noncommutative rings
UDC 512.5 Let $R$ be a noncommutative ring. The works by Hirano et al. and Groenewald (see [Bull. Korean Math. Soc., 47, No. 5, 1077–1087 (2010)] and [Int. Electron. J. Algebra, 28, 43–68 (2020)]), were devoted to the investigation of weakly prime ideals in noncommutative rings. In this work, we g...
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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/8391 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513066418962432 |
|---|---|
| author | Çay, Hatice Ersoy, Bayram Ali Çay, Hatice Ersoy, Bayram Ali |
| author_facet | Çay, Hatice Ersoy, Bayram Ali Çay, Hatice Ersoy, Bayram Ali |
| author_sort | Çay, Hatice |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-03-21T13:38:30Z |
| description | UDC 512.5
Let $R$ be a noncommutative ring. The works by Hirano et al. and Groenewald (see [Bull. Korean Math. Soc., 47, No. 5, 1077–1087 (2010)] and [Int. Electron. J. Algebra, 28, 43–68 (2020)]), were devoted to the investigation of weakly prime ideals in noncommutative rings. In this work, we generalize their findings by introducing the concept of $S$-weakly prime ideals via taking $S$ as an $m$-system, which is also a generalization of the concept of right $S$-prime ideals first introduced in [Mediterran. J. Math., 21, No. 2, Article 43 (2024)]. |
| doi_str_mv | 10.3842/umzh.v77i5.8391 |
| first_indexed | 2026-03-24T03:38:46Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-8391 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:38:46Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-83912026-03-21T13:38:30Z $S$-weakly prime ideals in noncommutative rings $S$-weakly prime ideals in noncommutative rings Çay, Hatice Ersoy, Bayram Ali Çay, Hatice Ersoy, Bayram Ali noncommutative rings s-prime ideals s-weakly prime ideals weakly prime ideals 16N60 16N49 UDC 512.5 Let $R$ be a noncommutative ring. The works by Hirano et al. and Groenewald (see [Bull. Korean Math. Soc., 47, No. 5, 1077–1087 (2010)] and [Int. Electron. J. Algebra, 28, 43–68 (2020)]), were devoted to the investigation of weakly prime ideals in noncommutative rings. In this work, we generalize their findings by introducing the concept of $S$-weakly prime ideals via taking $S$ as an $m$-system, which is also a generalization of the concept of right $S$-prime ideals first introduced in [Mediterran. J. Math., 21, No. 2, Article 43 (2024)]. УДК 512.5 $S$-слабко прості ідеали в некомутативних кільцях Нехай $R$ – некомутативне кільце. У роботах Хірано та ін. і Гроневальда (див. [Bull. Korean Math. Soc., 47, No. 5, 1077–1087 (2010)] і [Int. Electron. J. Algebra, 28, 43–68 (2020)]) проведено дослідження слабко простих ідеалів у некомутативних кільцях. Метою цієї роботи є узагальнення отриманих ними результатів шляхом уведення поняття $S$-слабко простих ідеалів за умови, що $S$ є $m$-системою. Це також є узагальненням поняття правих $S$-простих ідеалів, уперше запропонованого в [Mediterran. J. Math., 21, No. 2, Article 43 (2024)]. Institute of Mathematics, NAS of Ukraine 2026-03-21 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/8391 10.3842/umzh.v77i5.8391 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 5 (2025); 369–370 Український математичний журнал; Том 77 № 5 (2025); 369–370 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/8391/10527 Copyright (c) 2025 Hatice Çay, Bayram Ali Ersoy |
| spellingShingle | Çay, Hatice Ersoy, Bayram Ali Çay, Hatice Ersoy, Bayram Ali $S$-weakly prime ideals in noncommutative rings |
| title | $S$-weakly prime ideals in noncommutative rings |
| title_alt | $S$-weakly prime ideals in noncommutative rings |
| title_full | $S$-weakly prime ideals in noncommutative rings |
| title_fullStr | $S$-weakly prime ideals in noncommutative rings |
| title_full_unstemmed | $S$-weakly prime ideals in noncommutative rings |
| title_short | $S$-weakly prime ideals in noncommutative rings |
| title_sort | $s$-weakly prime ideals in noncommutative rings |
| topic_facet | noncommutative rings s-prime ideals s-weakly prime ideals weakly prime ideals 16N60 16N49 |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8391 |
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