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Lattice effect algebras densely embeddable into complete ones. (English) Zbl 1229.03056

The author studies MacNeille completions of effect algebras (as lattices). A necessary and sufficient condition for an Archimedean atomic lattice effect algebra is given such that its operation might be extended to its MacNeille completion to obtain a complete lattice effect algebra. Moreover, it is shown that there is at most one such extension.

MSC:

03G12 Quantum logic
06B23 Complete lattices, completions
06C15 Complemented lattices, orthocomplemented lattices and posets
06D35 MV-algebras
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References:

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