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Effect Algebras Which Can Be Covered by MV-Algebras

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Abstract

We exhibit effect algebras which can be covered by MV-subalgebras. We show that any effect algebra E which satisfies the Riesz interpolation property (RIP) and the so-called difference-meet property (DMP) can be covered by blocks, maximal subsets of mutually strongly compatible elements of E, which are always MV-subalegbras. This result generalizes that of Riečanová who proved the same result for lattice-ordered effect algebras. We show that for effect algebras with only (RIP) the result in question can fail.

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Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, SK-814 73, Bratislava, Slovakia

    Anatolij Dvurečenskij

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  1. Anatolij Dvurečenskij
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Dvurečenskij, A. Effect Algebras Which Can Be Covered by MV-Algebras. International Journal of Theoretical Physics 41, 221–229 (2002). https://doi.org/10.1023/A:1014002721731

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  • DOI: https://doi.org/10.1023/A:1014002721731

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