Archimedean Atomic Lattice Effect Algebras with Complete Lattice of Sharp Elements
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چکیده
منابع مشابه
Archimedean Atomic Lattice Effect Algebras with Complete Lattice of Sharp Elements
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 algebras. Moreover, we prove that if such effect algebra E is separable and modular then there exists a faithful state on E. Further, if an atomic lattice effect algebra is densely embeddable into a c...
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For every central element z of a lattice effect algebra E, the interval [0, z] with the ⊕ operation inherited from E and the new unity z is a lattice effect algebra in its own right. We show connections between blocks, sharp elements and central elements of [0, z] and those of E. We prove that except for central elements, the intervals [0, z] are closed with respect to the ⊕-operation also for ...
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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 b E of E there exists an effect algebraic partial binary operation b ⊕ then b ⊕ need not be an extension of ⊕. Moreover, for an Archimedean atomic lattice effect algebra E we give a necessary and sufficient condition for ...
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ژورنال
عنوان ژورنال: Symmetry, Integrability and Geometry: Methods and Applications
سال: 2010
ISSN: 1815-0659
DOI: 10.3842/sigma.2010.001