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On (finite) distributive lattices with antitone involutions

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Abstract

Distributive lattices with antitone involutions (or equivalently, distributive basic algebras) are studied. It is proved that in the finite case their underlying lattices are isomorphic to direct products of finite chains, and hence finite distributive basic algebras can be constructed by “perturbing” finite MV-algebras, and moreover, under certain natural conditions, they even coincide with finite MV-algebras. Sharp elements in basic algebras satisfying these natural conditions are studied, too.

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Acknowledgments

We would like to thank the referees for their valuable comments that helped to improve the paper.

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Authors and Affiliations

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

    Michal Botur & Jan Kühr

Authors
  1. Michal Botur
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  2. Jan Kühr
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Corresponding author

Correspondence to Jan Kühr.

Additional information

Communicated by L. G. Lacasa.

This work has been supported by the ESF project CZ.1.07/2.3.00/20.0051 “Algebraic Methods in Quantum Logic”, by the GAČR project P201/11/P346 “Non-associative Residuated Structures”, and by the Palacký University project PrF 2013 033 “Mathematical Structures”

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Botur, M., Kühr, J. On (finite) distributive lattices with antitone involutions. Soft Comput 18, 1033–1040 (2014). https://doi.org/10.1007/s00500-013-1205-5

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  • DOI: https://doi.org/10.1007/s00500-013-1205-5

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