| Title:
|
0-distributive posets (English) |
| Author:
|
Mokbel, Khalid A. |
| Author:
|
Kharat, Vilas S. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
138 |
| Issue:
|
3 |
| Year:
|
2013 |
| Pages:
|
325-335 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Several characterizations of 0-distributive posets are obtained by using the prime ideals as well as the semiprime ideals. It is also proved that if every proper $l$-filter of a poset is contained in a proper semiprime filter, then it is $0$-distributive. Further, the concept of a semiatom in 0-distributive posets is introduced and characterized in terms of dual atoms and also in terms of maximal annihilator. Moreover, semiatomic 0-distributive posets are defined and characterized. It is shown that a $0$-distributive poset $P$ is semiatomic if and only if the intersection of all non dense prime ideals of $P$ equals $(0]$. Some counterexamples are also given. (English) |
| Keyword:
|
0-distributive poset |
| Keyword:
|
ideal |
| Keyword:
|
semiprime ideal |
| Keyword:
|
prime ideal |
| Keyword:
|
semiatom |
| Keyword:
|
semiatomic 0-distributive poset |
| MSC:
|
06A06 |
| MSC:
|
06A75 |
| MSC:
|
06D75 |
| idZBL:
|
Zbl 06260036 |
| idMR:
|
MR3136500 |
| DOI:
|
10.21136/MB.2013.143440 |
| . |
| Date available:
|
2013-09-14T11:49:39Z |
| Last updated:
|
2023-10-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143440 |
| . |
| Reference:
|
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| . |
