Geodesic
Lattice effect algebras densely embeddable into complete ones
Kybernetika, Tome 47 (2011) no. 1, pp. 100-109

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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.
Classification : 03G12, 06D35, 06F25, 81P10
Keywords: non-classical logics; orthomodular lattices; effect algebras; $MV$-algebras; MacNeille completions 
@article{KYB_2011__47_1_a7,
     author = {Rie\v{c}anov\'a, Zdenka},
     title = {Lattice effect algebras densely embeddable into complete ones},
     journal = {Kybernetika},
     pages = {100--109},
     publisher = {mathdoc},
     volume = {47},
     number = {1},
     year = {2011},
     mrnumber = {2807867},
     zbl = {1229.03056},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2011__47_1_a7/}
}
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Riečanová, Zdenka. Lattice effect algebras densely embeddable into complete ones. Kybernetika, Tome 47 (2011) no. 1, pp. 100-109. http://geodesic.mathdoc.fr/item/KYB_2011__47_1_a7/