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The Variety of Lattice Effect Algebras Generated by MV-algebras and the Horizontal Sum of Two 3-element Chains

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Abstract

It has been recently shown [4] that the lattice effect algebras can be treated as a subvariety of the variety of so-called basic algebras. The open problem whether all subdirectly irreducible distributive lattice effect algebras are just subdirectly irreducible MV-chains and the horizontal sum \({\mathcal{H}}\) of two 3-element chains is in the paper transferred into a more tractable one. We prove that modulo distributive lattice effect algebras, the variety generated by MV-algebras and \({\mathcal{H}}\) is definable by three simple identities and the problem now is to check if these identities are satisfied by all distributive lattice effect algebras or not.

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Authors and Affiliations

  1. Department of Algebra and Geometry, Palacký University Olomouc, Tomkova 40, 779 00, Olomouc, Czech Republic

    Radomír Halaš

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  1. Radomír Halaš
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Correspondence to Radomír Halaš.

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Halaš, R. The Variety of Lattice Effect Algebras Generated by MV-algebras and the Horizontal Sum of Two 3-element Chains. Stud Logica 89, 19–35 (2008). https://doi.org/10.1007/s11225-008-9115-8

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  • DOI: https://doi.org/10.1007/s11225-008-9115-8

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