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The Join of the Variety of MV-Algebras and the Variety of Orthomodular Lattices

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Abstract

We axiomatize the smallest variety that contains both the variety of MV-algebras and the variety (term equivalent to the variety) of orthomodular lattices.

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Notes

  1. In fact, ⊕ is commutative iff it is associative, which happens exactly in MV-algebras.

  2. In the literature on (lattice) effect algebras, the name “ideal” is often used for subsets which are closed with respect to + and downwards closed, while our ideals defined above correspond to the so-called “Riesz ideals”.

  3. By an additive term we mean a term built up from the variables using the addition ⊕ only.

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Acknowledgments

This work has been supported by the Palacký University project IGA PrF 2014016 “Mathematical Structures” and by the MOBILITY project 7AMB13AT005 “Partially Ordered Algebraic Systems and Algebras”. The first author has also been supported by the Czech Science Foundation (GAČR) project 15-15286S “Algebraic, Many-valued and Quantum Structures for Uncertainty Modelling”.

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Authors and Affiliations

  1. Department of Algebra and Geometry, Faculty of Science, Palacký University in Olomouc, 17. listopadu 12, CZ-77146, Olomouc, Czech Republic

    Jan Kühr, Ivan Chajda & Radomír Halaš

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  1. Jan Kühr
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  2. Ivan Chajda
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  3. Radomír Halaš
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Correspondence to Jan Kühr.

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Kühr, J., Chajda, I. & Halaš, R. The Join of the Variety of MV-Algebras and the Variety of Orthomodular Lattices. Int J Theor Phys 54, 4423–4429 (2015). https://doi.org/10.1007/s10773-015-2619-x

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  • DOI: https://doi.org/10.1007/s10773-015-2619-x

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