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Congruence lattices of connected monounary algebras

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Abstract

The system of all congruences of an algebra (A, F) forms a lattice, denoted \({{\,\mathrm{Con}\,}}(A, F)\). Further, the system of all congruence lattices of all algebras with the base set A forms a lattice \(\mathcal {E}_A\). We deal with meet-irreducibility in \(\mathcal {E}_A\) for a given finite set A. All meet-irreducible elements of \(\mathcal {E}_A\) are congruence lattices of monounary algebras. Some types of meet-irreducible congruence lattices were already described. In the case when a monounary algebra (A, f) is connected, we prove necessary and sufficient condition under which \({{\,\mathrm{Con}\,}}(A, f)\) is \(\wedge \)-irreducible.

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Authors and Affiliations

  1. Institute of Mathematics, P.J. Šafárik University in Košice, Košice, Slovakia

    Danica Jakubíková-Studenovská & Lucia Janičková

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  1. Danica Jakubíková-Studenovská
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  2. Lucia Janičková
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Correspondence to Danica Jakubíková-Studenovská.

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Presented by R. Pöschel.

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This work was supported by Grant VEGA 1/0097/18.

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Jakubíková-Studenovská, D., Janičková, L. Congruence lattices of connected monounary algebras. Algebra Univers. 81, 54 (2020). https://doi.org/10.1007/s00012-020-00686-2

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  • DOI: https://doi.org/10.1007/s00012-020-00686-2

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