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Abstract. A planar semimodular lattice is slim if it does not contain $SM 3$ as a sublattice. An SPS lattice is a slim, planar, semimodular lattice. Congruence lattices of SPS lattices satisfy a number of properties. It was conjectured that these properties characterize them. A recent result of Gábor Czédli proves that there is an eight element (planar) distributive lattice having all these properties that cannot be represented as the congruence lattice of an SPS lattice. We provide a new proof.
DOI: 10.14232/actasm-014-024-1
AMS Subject Classification
(1991): 06C10, 06B10
Keyword(s):
fork extension,
join-irreducible congruence
Received March 28, 2014, and in revised from May 6, 2014. (Registered under 24/2014.)
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