| Title:
|
Relatively pseudocomplemented posets (English) |
| Author:
|
Chajda, Ivan |
| Author:
|
Länger, Helmut |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
143 |
| Issue:
|
1 |
| Year:
|
2018 |
| Pages:
|
89-97 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We extend the notion of a relatively pseudocomplemented meet-semilattice to arbitrary posets. We show some properties of the binary operation of relative pseudocomplementation and provide some corresponding characterizations. We show that relatively pseudocomplemented posets satisfying a certain simple identity in two variables are join-semilattices. Finally, we show that every relatively pseudocomplemented poset is distributive and that the converse holds for posets satisfying the ascending chain condition and one more natural condition. Suitable examples are provided. (English) |
| Keyword:
|
relatively pseudocomplemented poset |
| Keyword:
|
join-semilattice |
| Keyword:
|
distributive poset |
| MSC:
|
06A06 |
| MSC:
|
06A11 |
| MSC:
|
06D15 |
| idZBL:
|
Zbl 06861593 |
| idMR:
|
MR3778051 |
| DOI:
|
10.21136/MB.2017.0037-16 |
| . |
| Date available:
|
2018-03-19T10:35:15Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147143 |
| . |
| 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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| Reference:
|
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| . |
