Displaying similar documents to “The existence of states on every Archimedean atomic lattice effect algebra with at most five blocks”

Archimedean atomic lattice effect algebras in which all sharp elements are central

Zdena Riečanová (2006)

Kybernetika

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We prove that every Archimedean atomic lattice effect algebra the center of which coincides with the set of all sharp elements is isomorphic to a subdirect product of horizontal sums of finite chains, and conversely. We show that every such effect algebra can be densely embedded into a complete effect algebra (its MacNeille completion) and that there exists an order continuous state on it.

An atomic MV-effect algebra with non-atomic center

Vladimír Olejček (2007)

Kybernetika

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Does there exist an atomic lattice effect algebra with non-atomic subalgebra of sharp elements? An affirmative answer to this question (and slightly more) is given: An example of an atomic MV-effect algebra with a non-atomic Boolean subalgebra of sharp or central elements is presented.