| Title:
|
On minimal ideals in the ring of real-valued continuous functions on a frame (English) |
| Author:
|
Karimi Feizabadi, Abolghasem |
| Author:
|
Estaji, Ali Akbar |
| Author:
|
Abedi, Mostafa |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
54 |
| Issue:
|
1 |
| Year:
|
2018 |
| Pages:
|
1-13 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\mathcal{R}L$ be the ring of real-valued continuous functions on a frame $L$. The aim of this paper is to study the relation between minimality of ideals $I$ of $\mathcal{R}L$ and the set of all zero sets in $L$ determined by elements of $I$. To do this, the concepts of coz-disjointness, coz-spatiality and coz-density are introduced. In the case of a coz-dense frame $L$, it is proved that the $f$-ring $\mathcal{R}L$ is isomorphic to the $f$-ring $ C(\Sigma L)$ of all real continuous functions on the topological space $\Sigma L$. Finally, a one-one correspondence is presented between the set of isolated points of $\Sigma L$ and the set of atoms of $L$. (English) |
| Keyword:
|
ring of real-valued continuous functions on a frame |
| Keyword:
|
coz-disjoint |
| Keyword:
|
coz-dense and coz-spatial frames |
| Keyword:
|
zero sets in pointfree topology |
| Keyword:
|
$z$-ideal |
| Keyword:
|
strongly $z$-ideal |
| MSC:
|
06D22 |
| MSC:
|
13A15 |
| MSC:
|
54C30 |
| idZBL:
|
Zbl 06861554 |
| idMR:
|
MR3783288 |
| DOI:
|
10.5817/AM2018-1-1 |
| . |
| Date available:
|
2018-03-12T13:41:49Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147104 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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