| Title:
|
$\alpha $-ideals in $0$-distributive posets (English) |
| Author:
|
Mokbel, Khalid A. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
140 |
| Issue:
|
3 |
| Year:
|
2015 |
| Pages:
|
319-328 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The concept of $\alpha $-ideals in posets is introduced. Several properties of $\alpha $-ideals in $0$-distributive posets are studied. Characterization of prime ideals to be $\alpha $-ideals in $0$-distributive posets is obtained in terms of minimality of ideals. Further, it is proved that if a prime ideal $I$ of a $0$-distributive poset is non-dense, then $I$ is an $\alpha $-ideal. Moreover, it is shown that the set of all $\alpha $-ideals $\alpha \mathop {\rm Id}(P)$ of a poset $P$ with $0$ forms a complete lattice. A result analogous to separation theorem for finite $0$-distributive posets is obtained with respect to prime $\alpha $-ideals. Some counterexamples are also given. (English) |
| Keyword:
|
$0$-distributive poset |
| Keyword:
|
ideal |
| Keyword:
|
$\alpha $-ideal |
| Keyword:
|
prime ideal |
| Keyword:
|
non-dense ideal |
| Keyword:
|
minimal ideal |
| Keyword:
|
annihilator ideal |
| MSC:
|
06A06 |
| MSC:
|
06A75 |
| idZBL:
|
Zbl 06486942 |
| idMR:
|
MR3397260 |
| DOI:
|
10.21136/MB.2015.144398 |
| . |
| Date available:
|
2015-09-03T10:52:59Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144398 |
| . |
| 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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| . |
