Congruence lattices of $2$-valued unary algebras

@misc{dorman2026congruence,
  title = {{Congruence lattices of $2$-valued unary algebras}},
  author = {Miklós Dormán and Kamilla Kátai-Urbán and Eszter K. Horváth and Tamás Waldhauser},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33305},
  eprint = {2610.33305},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33305},
}

TY  - UNPB
TI  - Congruence lattices of $2$-valued unary algebras
AU  - Miklós Dormán
AU  - Kamilla Kátai-Urbán
AU  - Eszter K. Horváth
AU  - Tamás Waldhauser
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.33305
UR  - https://arxiv.org/abs/2610.33305
AB  - 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.
ER  -