| Title:
|
Primeness and semiprimeness in posets (English) |
| Author:
|
Kharat, Vilas S. |
| Author:
|
Mokbel, Khalid A. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
134 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
19-30 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The concept of a semiprime ideal in a poset is introduced. Characterizations of semiprime ideals in a poset $P$ as well as characterizations of a semiprime ideal to be prime in $P$ are obtained in terms of meet-irreducible elements of the lattice of ideals of $P$ and in terms of maximality of ideals. Also, prime ideals in a poset are characterized. (English) |
| Keyword:
|
semiprime ideal |
| Keyword:
|
prime ideal |
| Keyword:
|
meet-irreducible element |
| Keyword:
|
$I$-atom |
| MSC:
|
06B10 |
| idZBL:
|
Zbl 1212.06001 |
| idMR:
|
MR2504684 |
| DOI:
|
10.21136/MB.2009.140636 |
| . |
| Date available:
|
2010-07-20T17:44:55Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140636 |
| . |
| 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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| . |
