Abstract. Let the finite distributive lattice $D$ be isomorphic to the congruence lattice of a finite lattice $L$. Let $Q$ denote those elements of $D$ that correspond to principal congruences under this isomorphism. Then $Q$ contains $0,1 \in D$ and all the join-irreducible elements of $D$. If $Q$ contains exactly these elements, we say that $L$ is a minimal representation of $D$ by principal congruences of the lattice $L$. We characterize finite distributive lattices $D$ with a minimal representation by principal congruences with the property that $D$ has at most two dual atoms.
DOI: 10.14232/actasm-017-060-9
AMS Subject Classification
(1991): 06B10, 06A06
Keyword(s):
finite lattice,
principal congruence,
ordered set
Received October 10, 2017, and in revised form November 26, 2017. (Registered under 60/2017.)
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