| Title:
|
On the mappings ${\mathcal Z}_A$ and $\Im_A$ in intermediate rings of $C(X)$ (English) |
| Author:
|
Parsinia, Mehdi |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
59 |
| Issue:
|
3 |
| Year:
|
2018 |
| Pages:
|
383-390 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this article, we investigate new topological descriptions for two well-known mappings ${\mathcal Z}_A$ and $\Im_A$ defined on intermediate rings $A(X)$ of $C(X)$. Using this, coincidence of each two classes of $z$-ideals, ${\mathcal Z}_A$-ideals and $\Im_A$-ideals of $A(X)$ is studied. Moreover, we answer five questions concerning the mapping $\Im_A$ raised in [J. Sack, S. Watson, {$C$ and $C^*$ among intermediate rings}, Topology Proc. {43} (2014), 69--82]. (English) |
| Keyword:
|
$z$-ideal |
| Keyword:
|
${\mathcal Z}_A$-ideal |
| Keyword:
|
$\Im_A$-ideal |
| Keyword:
|
$z$-filter |
| Keyword:
|
${\mathcal Z}_A$-filter |
| Keyword:
|
$\Im_A$-filter |
| Keyword:
|
intermediate ring |
| MSC:
|
46E25 |
| MSC:
|
54C30 |
| idZBL:
|
Zbl 06940878 |
| idMR:
|
MR3861560 |
| DOI:
|
10.14712/1213-7243.2015.249 |
| . |
| Date available:
|
2018-09-10T12:17:50Z |
| Last updated:
|
2020-10-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147405 |
| . |
| Reference:
|
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| Reference:
|
[2] Aliabad A. R., Parsinia M.: $z_R$-ideals and $z_R^{\circ}$-ideals in subrings of $ {\mathbb R}^X$.to appear in Iranian J. Math. Sci. Inform. |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| . |
