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arXiv · 2610.33305

Congruence lattices of $2$-valued unary algebras

Miklós Dormán·Kamilla Kátai-Urbán·Eszter K. Horváth·Tamás Waldhauser
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Abstract

We study congruence lattices of finite algebras whose basic operations are unary and have exactly two values. We prove that the class of finite lattices representable in this way is closed under taking filters, glued sums and ordinal sums, and direct products with finite distributive lattices, but it is not closed under taking ideals or arbitrary direct products. A classification of lattices with at most seven elements with respect to representability is also presented.

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Miklós Dormán, Kamilla Kátai-Urbán, Eszter K. Horváth, Tamás Waldhauser. 2026-10-23. Congruence lattices of $2$-valued unary algebras. https://arxiv.org/abs/2610.33305

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