Article
| Title: | The clean elements of the ring $\mathcal R(L)$ (English) |
| Author: | Estaji, Ali Akbar |
| Author: | Taha, Maryam |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 74 |
| Issue: | 1 |
| Year: | 2024 |
| Pages: | 211-230 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We characterize clean elements of $\mathcal R(L)$ and show that $\alpha \in \mathcal {R}(L)$ is clean if and only if there exists a clopen sublocale $U$ in $L$ such that $\frak {c}_L({\rm coz} (\alpha - {\bf 1})) \subseteq U \subseteq \frak {o}_L( {\rm coz} (\alpha ))$. Also, we prove that $\mathcal R(L)$ is clean if and only if $\mathcal R(L)$ has a clean prime ideal. Then, according to the results about $\mathcal R(L),$ we immediately get results about $\mathcal C_{c}(L).$ (English) |
| Keyword: | frame |
| Keyword: | ring of real-valued continuous function |
| Keyword: | strongly zero-dimensional |
| Keyword: | clean element |
| Keyword: | sublocale |
| MSC: | 06D22 |
| MSC: | 54C05 |
| MSC: | 54C30 |
| idZBL: | Zbl 07893375 |
| idMR: | MR4717830 |
| DOI: | 10.21136/CMJ.2023.0062-23 |
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| Date available: | 2024-03-13T10:08:11Z |
| Last updated: | 2024-12-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152276 |
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