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Minimal relation algebras

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Abstract

This paper is concerned with the covers of the atoms in the lattice of varieties of relation algebras. Aminimal relation algebra is one that is simple and generates such a subvariety. The main result we prove is that there are exactly three finite minimal relation algebras that aretotally symmetric (i.e., satisfy the identitiesx=x andx ≤ x; x). We also give an example of an infinite minimal totally symmetric relation algebra, and some results about other subvarieties.

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Authors and Affiliations

  1. Department of Mathematics, Vanderbilt University, 37235, Nashville, TN, USA

    P. Jipsen & E. Lukács

  2. Department of Mathematics, Technical University, 1111, Budapest, Hungary

    P. Jipsen & E. Lukács

Authors
  1. P. Jipsen
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  2. E. Lukács
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Dedicated to Bjarni Jonsson on his 70th birthday

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Jipsen, P., Lukács, E. Minimal relation algebras. Algebra Universalis 32, 189–203 (1994). https://doi.org/10.1007/BF01191538

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  • DOI: https://doi.org/10.1007/BF01191538

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