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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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