Title:
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Lattice effect algebras densely embeddable into complete ones (English) |
Author:
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Riečanová, Zdenka |
Language:
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English |
Journal:
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Kybernetika |
ISSN:
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0023-5954 |
Volume:
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47 |
Issue:
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1 |
Year:
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2011 |
Pages:
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100-109 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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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:
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non-classical logics |
Keyword:
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orthomodular lattices |
Keyword:
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effect algebras |
Keyword:
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$MV$-algebras |
Keyword:
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MacNeille completions |
MSC:
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03G12 |
MSC:
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06D35 |
MSC:
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06F25 |
MSC:
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81P10 |
idZBL:
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Zbl 1229.03056 |
idMR:
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MR2807867 |
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Date available:
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2011-04-12T13:07:40Z |
Last updated:
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2013-09-22 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/141481 |
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Reference:
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