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Varieties of semiassociative relation algebras and tense algebras

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Abstract

It is well known that the subvariety lattice of the variety of relation algebras has exactly three atoms. The (join-irreducible) covers of two of these atoms are known, but a complete classification of the (join-irreducible) covers of the remaining atom has not yet been found. These statements are also true of a related subvariety lattice, namely the subvariety lattice of the variety of semiassociative relation algebras. The present article shows that this atom has continuum many covers in this subvariety lattice (and in some related subvariety lattices) using a previously established term equivalence between a variety of tense algebras and a variety of semiassociative \(r\)-algebras.

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Acknowledgements

The first author would like to thank Peter Jipsen for recommending [13], and Eli Hazel for solving a mysterious \(\hbox{\LaTeX}\) issue.

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  1. Department of Mathematics and Statistics, La Trobe University, Bundoora, VIC, 3086, Australia

    James M. Koussas & Tomasz Kowalski

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  1. James M. Koussas
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  2. Tomasz Kowalski
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Correspondence to James M. Koussas.

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Presented by Peter Jipsen.

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Koussas, J.M., Kowalski, T. Varieties of semiassociative relation algebras and tense algebras. Algebra Univers. 81, 21 (2020). https://doi.org/10.1007/s00012-020-0646-9

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