Geodesic
Revisiting the Representation Theorem of Finite Distributive Lattices with Principal Congruences. A Proof-By-Picture Approach
Discussiones Mathematicae. General Algebra and Applications, Tome 41 (2021) no. 2, pp. 411-417

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A classical result of R.P. Dilworth states that every finite distributive lattice D can be represented as the congruence lattice of a finite lattice L. A sharper form was published in G. Grätzer and E.T. Schmidt in 1962, adding the requirement that all congruences in L be principal. Another variant, published in 1998 by the authors and E.T. Schmidt, constructs a planar semimodular lattice L. In this paper, we merge these two results: we construct L as a planar semimodular lattice in which all congruences are principal. This paper relies on the techniques developed by the authors and E.T. Schmidt in the 1998 paper.
Keywords: principal congruence, finite distributive lattice 
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Grätzer, G.; Lakser, H. Revisiting the Representation Theorem of Finite Distributive Lattices with Principal Congruences. A Proof-By-Picture Approach. Discussiones Mathematicae. General Algebra and Applications, Tome 41 (2021) no. 2, pp. 411-417. http://geodesic.mathdoc.fr/item/DMGAA_2021_41_2_a12/