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Abstract. For a finite distributive lattice $D$, let us call $Q \ci D$ \emph{principal congruence representable}, if there is a finite lattice $L$ such that the congruence lattice of $L$ is isomorphic to $D$ and the principal congruences of $L$ correspond to $Q$ under this isomorphism. We find a necessary condition for representability by principal congruences and prove that for finite distributive lattices with a join-irreducible unit element this condition is also sufficient.
DOI: 10.14232/actasm-017-036-7
AMS Subject Classification
(1991): 06B10
Keyword(s):
congruence lattice,
principal congruence,
join-irreducible congruence,
finite distributive lattice,
principal congruence representable set
Received May 22, 2017, and in revised form August 1, 2017. (Registered under 36/2017.)
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