• Corpus ID: 26619089

Lattice effect algebras densely embeddable into complete ones

@article{Riecanov2011LatticeEA,
  title={Lattice effect algebras densely embeddable into complete ones},
  author={Zdenka Riecanov{\'a}},
  journal={Kybernetika},
  year={2011},
  volume={47},
  pages={100-109}
}
  • 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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Mac Neille completion of centers and centers of Mac Neille completions of lattice effect algebras

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Smearings of States Defined on Sharp Elements Onto Effect Algebras

It is shown that if E is complete, atomic, and (o)-continuous, then a state on E exists iff there exists a state in S(E), and that such an effect algebra E is an algebraic lattice compactly generated by finite elements of E.

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.

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An application proves a theorem about subdirect decompositions of lattice effect algebras and proves a statement about the existence of subadditive state on some block-finite effect alGEbras.

On central atoms of Archimedean atomic lattice effect algebras

It is shown that there exists a lattice effect algebra (E, ⊕, 0, 1) with atomic C(E) which is not a bifull sublattice of E.

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

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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

ARCHIMEDEAN AND BLOCK-FINITE LATTICE EFFECT ALGEBRAS

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