• Corpus ID: 26619089

Lattice effect algebras densely embeddable into complete ones

  title={Lattice effect algebras densely embeddable into complete ones},
  author={Zdenka Riecanov{\'a}},
  • Z. Riecanová
  • Published 2011
  • Computer Science, Mathematics
  • Kybernetika
An effect algebraic partial binary operation ⊕ 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… 

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S-Dominating Effect Algebras

It is shown that an S-dominating effect algebra P has a naturally defined Brouwer-complementation that gives P the structure of a Brou Wer–Zadeh poset, and it is proved that the sharp elements of P form anorthomodular lattice.

Subdirect Decompositions of Lattice Effect Algebras

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On central atoms of Archimedean atomic lattice effect algebras

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Generalization of Blocks for D-Lattices and Lattice-Ordered Effect Algebras

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Effect algebras and unsharp quantum logics

The effects in a quantum-mechanical system form a partial algebra and a partially ordered set which is the prototypical example of the effect algebras discussed in this paper. The relationships among


1. Basic definitions Effect algebras (introduced by Foulis D.J. and Bennett M.K. in [7], 1994) are important for modelling unsharp measurements in Hilbert space: The set of all effects is the set of