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} }
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…
2 Citations
Two Remarks to Bifullness of Centers of Archimedean Atomic Lattice Effect Algebras
- Mathematics, Computer Science
- 2011
It is shown that for atomic lattice effect algebras E (atomic orthomodular lattices) neither completeness (and atomicity) of C(E) nor σ -completeness of E are sufficient conditions for C( E) to be a bifull sublattice of E .
Mac Neille completion of centers and centers of Mac Neille completions of lattice effect algebras
- MathematicsKybernetika
- 2010
It is shown that even the completeness of $C(E)$ and its bifullness in $E$ is not sufficient to guarantee the mentioned equality, and a necessary condition under which the equality may hold is found.
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We study Archimedean atomic lattice effect algebras whose set of sharp elements is a complete lattice. We show properties of centers, compatibility centers and central atoms of such lattice effect…
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