| Title:
|
Lattice effect algebras densely embeddable into complete ones (English) |
| Author:
|
Riečanová, Zdenka |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
47 |
| Issue:
|
1 |
| Year:
|
2011 |
| Pages:
|
100-109 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
An effect algebraic partial binary operation $øplus$ defined on the underlying set $E$ uniquely introduces partial order, but not conversely. We show that if on a MacNeille completion $\widehat{E}$ of $E$ there exists an effect algebraic partial binary operation $\widehat{\oplus}$ then $\widehat{\oplus}$ need not be an extension of ${\oplus}$. Moreover, for an Archimedean atomic lattice effect algebra $E$ we give a necessary and sufficient condition for that $\widehat{\oplus}$ existing on $\widehat{E}$ is an extension of ${\oplus}$ defined on $E$. Further we show that such $\widehat{\oplus}$ extending ${\oplus}$ exists at most one. (English) |
| Keyword:
|
non-classical logics |
| Keyword:
|
orthomodular lattices |
| Keyword:
|
effect algebras |
| Keyword:
|
$MV$-algebras |
| Keyword:
|
MacNeille completions |
| MSC:
|
03G12 |
| MSC:
|
06D35 |
| MSC:
|
06F25 |
| MSC:
|
81P10 |
| idZBL:
|
Zbl 1229.03056 |
| idMR:
|
MR2807867 |
| . |
| Date available:
|
2011-04-12T13:07:40Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141481 |
| . |
| Reference:
|
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