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Monounary algebras containing subalgebras with meet-irreducible congruence lattice

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Abstract

The system of all congruence lattices of all algebras with fixed base set A forms a lattice with respect to inclusion, denoted by \(\mathcal {E}_A\). Let A be finite. The meet-irreducible elements of \(\mathcal {E}_A\) are congruence lattices of monounary algebras. We assume that (A, f) has a connected subalgebra B such that B contains at least 3 cyclic elements and is meet-irreducible in \({\mathcal {E}}_B\) and we prove several sufficient conditions under which \({{\,\mathrm{Con}\,}}(A, f)\) is meet-irreducible in \({\mathcal {E}}_A\).

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Acknowledgements

We would like to thank the reviewer of this paper for a thoughtful review and helpful remarks.

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  1. Institute of Mathematics, P.J. Šafárik University in Košice, Jesenná 5, 040 01, Košice, Slovakia

    Lucia Janičková

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  1. Lucia Janičková
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Correspondence to Lucia Janičková.

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Presented by M. Ploščica.

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This work was supported by Project vvgs-pf-2020-1426 and Grant VEGA 1/0152/22.

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Janičková, L. Monounary algebras containing subalgebras with meet-irreducible congruence lattice. Algebra Univers. 83, 36 (2022). https://doi.org/10.1007/s00012-022-00786-1

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  • DOI: https://doi.org/10.1007/s00012-022-00786-1

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