Displaying similar documents to “An atomic MV-effect algebra with non-atomic center”

The existence of states on every Archimedean atomic lattice effect algebra with at most five blocks

Zdena Riečanová (2008)

Kybernetika

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Effect algebras are very natural logical structures as carriers of probabilities and states. They were introduced for modeling of sets of propositions, properties, questions, or events with fuzziness, uncertainty or unsharpness. Nevertheless, there are effect algebras without any state, and questions about the existence (for non-modular) are still unanswered. We show that every Archimedean atomic lattice effect algebra with at most five blocks (maximal MV-subalgebras) has at least one...

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.

Isometries of generalized M V -algebras

Ján Jakubík (2007)

Czechoslovak Mathematical Journal

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In this paper we investigate the relations between isometries and direct product decompositions of generalized M V -algebras.

A characterization of commutative basic algebras

Ivan Chajda (2009)

Mathematica Bohemica

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A basic algebra is an algebra of the same type as an MV-algebra and it is in a one-to-one correspondence to a bounded lattice having antitone involutions on its principal filters. We present a simple criterion for checking whether a basic algebra is commutative or even an MV-algebra.