Article
| Title: | On wsq-primary ideals (English) |
| Author: | Aslankarayiğit Uğurlu, Emel |
| Author: | Bouba, El Mehdi |
| Author: | Tekir, Ünsal |
| Author: | Koç, Suat |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 73 |
| Issue: | 2 |
| Year: | 2023 |
| Pages: | 415-429 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We introduce weakly strongly quasi-primary (briefly, wsq-primary) ideals in commutative rings. Let $R$ be a commutative ring with a nonzero identity and $Q$ a proper ideal of $R$. The proper ideal $Q$ is said to be a weakly strongly quasi-primary ideal if whenever $0\neq ab\in Q$ for some $a,b\in R$, then $a^{2}\in Q$ or $b\in \sqrt {Q}.$ Many examples and properties of wsq-primary ideals are given. Also, we characterize nonlocal Noetherian von Neumann regular rings, fields, nonlocal rings over which every proper ideal is wsq-primary, and zero dimensional rings over which every proper ideal is wsq-primary. Finally, we study finite union of wsq-primary ideals. (English) |
| Keyword: | primary ideal |
| Keyword: | weakly primary ideal |
| Keyword: | quasi-primary ideal |
| Keyword: | weakly 2-prime ideal |
| Keyword: | strongly quasi-primary ideal |
| MSC: | 05C25 |
| MSC: | 13A15 |
| MSC: | 13A99 |
| MSC: | 13F30 |
| idZBL: | Zbl 07729515 |
| idMR: | MR4586902 |
| DOI: | 10.21136/CMJ.2023.0259-21 |
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| Date available: | 2023-05-04T17:44:24Z |
| Last updated: | 2023-09-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151665 |
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