| Title:
|
$0$-ideals in $0$-distributive posets (English) |
| Author:
|
Mokbel, Khalid A. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
141 |
| Issue:
|
4 |
| Year:
|
2016 |
| Pages:
|
509-517 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The concept of a $0$-ideal in \mbox {$0$-distributive} posets is introduced. Several properties of $0$-ideals in $0$-distributive posets are established. Further, the interrelationships between $0$-ideals and \mbox {$\alpha $-ideals} in \mbox {$0$-distributive} posets are investigated. Moreover, a characterization of prime ideals to be $0$-ideals in $0$-distributive posets is obtained in terms of non-dense ideals. It is shown that every $0$-ideal of a $0$-distributive meet semilattice is semiprime. Several counterexamples are discussed. (English) |
| Keyword:
|
$0$-distributive poset |
| Keyword:
|
$0$-ideal |
| Keyword:
|
$\alpha $-ideal |
| Keyword:
|
prime ideal |
| Keyword:
|
semiprime ideal |
| Keyword:
|
dense ideal |
| MSC:
|
06A06 |
| MSC:
|
06A75 |
| idZBL:
|
Zbl 06674860 |
| idMR:
|
MR3576797 |
| DOI:
|
10.21136/MB.2016.0028-14 |
| . |
| Date available:
|
2017-01-03T15:19:11Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145957 |
| . |
| 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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| . |
