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Lattice effect algebras densely embeddable into complete ones

Zdena Riečanová (2011)

Kybernetika

An effect algebraic partial binary operation ø p l u s defined on the underlying set E uniquely introduces partial order, but not conversely. We show that if on a MacNeille completion E ^ of E there exists an effect algebraic partial binary operation ^ then ^ need not be an extension of . Moreover, for an Archimedean atomic lattice effect algebra E we give a necessary and sufficient condition for that ^ existing on E ^ is an extension of defined on E . Further we show that such ^ extending exists at most...

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