# Some preliminary results on the set of principal congruences of a finite lattice

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## Abstract

In the second edition of the congruence lattice book, Problem 22.1 asks for a characterization of subsets *Q* of a finite distributive lattice *D* such that there is a finite lattice *L* whose congruence lattice is isomorphic to *D* and under this isomorphism *Q* corresponds the the principal congruences of *L*. In this note, we prove some preliminary results.

## Keywords

Congruence lattice Principal congruence Join-irreducible congruence Principal congruence representable set## Mathematics Subject Classification

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