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Mac Neille completion of centers and centers of Mac Neille completions of lattice effect algebras. (English) Zbl 1221.06010
The author extends his construction from [M. Kalina, “On central atoms of Archimedean atomic lattice effect algebras”, Kybernetika 46, No. 4, 609–620 (2010; Zbl 1214.06002)] and studies the following question: Let \(E\) be a lattice effect algebra. Is the MacNeille completion of the center of \(E\) equal to the center of the MacNeille completion of \(E\)? He presents a negative answer and a necessary condition under which the equality holds. Moreover, he shows that even the completeness and bifullness of the center of \(E\) is not sufficient for this.

MSC:
06C15 Complemented lattices, orthocomplemented lattices and posets
03G12 Quantum logic
06D35 MV-algebras
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
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References:
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