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arXiv · 2104.13843

Notes on planar semimodular lattices. VIII. Congruence lattices of SPS lattices

G. Grätzer
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Abstract

In this note, I find a new property of the congruence lattice, Con$L$, of an SPS lattice $L$ (slim, planar, semimodular, where "slim" is the absence of~$\mathsf M_3$ sublattices) with more than $2$ elements: \emph{there are at least two dual atoms in Con$L$}. So the three-element chain cannot be represented as the congruence lattice of an SPS lattice, supplementing a~result of G. Cz\'edli.

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G. Grätzer. 2021-04-28. Notes on planar semimodular lattices. VIII. Congruence lattices of SPS lattices. https://arxiv.org/abs/2104.13843

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