$S$-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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| Date: | 2026 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2026
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/8391 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | 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)]. |
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| DOI: | 10.3842/umzh.v77i5.8391 |