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On identities in orthocomplemented difference lattices

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Mathematica Slovaca

Abstract

In this note we continue the investigation of algebraic properties of orthocomplemented (symmetric) difference lattices (ODLs) as initiated and previously studied by the authors. We take up a few identities that we came across in the previous considerations. We first see that some of them characterize, in a somewhat non-trivial manner, the ODLs that are Boolean. In the second part we select an identity peculiar for set-representable ODLs. This identity allows us to present another construction of an ODL that is not set-representable. We then give the construction a more general form and consider algebraic properties of the ‘orthomodular support’.

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Authors and Affiliations

  1. Ruská 22, CZ-101 00, Prague 10, Czech Republic

    Milan Matoušek

  2. Department of Mathematics, Czech Technical University Faculty of Electrical Engineering, CZ-166 27, Prague 6, Czech Republic

    Pavel Pták

Authors
  1. Milan Matoušek
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  2. Pavel Pták
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Corresponding author

Correspondence to Milan Matoušek.

Additional information

Communicated by Anatolij Dvurečenskij

The authors acknowledge the support of the research plan MSM 0021620839 that is financed by the Ministry of Education of the Czech Republic and the grant GAČR 201/07/1051 of the Czech Grant Agency.

To Sylvia Pulmannová with compliments and admiration

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Matoušek, M., Pták, P. On identities in orthocomplemented difference lattices. Math. Slovaca 60, 583–590 (2010). https://doi.org/10.2478/s12175-010-0033-7

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  • DOI: https://doi.org/10.2478/s12175-010-0033-7

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