Geodesic
Archimedean atomic lattice effect algebras in which all sharp elements are central
Kybernetika, Tome 42 (2006) no. 2, pp. 143-150

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We prove that every Archimedean atomic lattice effect algebra the center of which coincides with the set of all sharp elements is isomorphic to a subdirect product of horizontal sums of finite chains, and conversely. We show that every such effect algebra can be densely embedded into a complete effect algebra (its MacNeille completion) and that there exists an order continuous state on it.
Classification : 03G10, 03G12, 03G25, 06D35, 81P10
Keywords: lattice effect algebra; sharp and central element; block; state; subdirect decomposition; MacNeille completion 
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     author = {Rie\v{c}anov\'a, Zdenka},
     title = {Archimedean atomic lattice effect algebras in which all sharp elements are central},
     journal = {Kybernetika},
     pages = {143--150},
     publisher = {mathdoc},
     volume = {42},
     number = {2},
     year = {2006},
     mrnumber = {2241781},
     zbl = {1249.03121},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2006__42_2_a1/}
}
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Riečanová, Zdenka. Archimedean atomic lattice effect algebras in which all sharp elements are central. Kybernetika, Tome 42 (2006) no. 2, pp. 143-150. http://geodesic.mathdoc.fr/item/KYB_2006__42_2_a1/