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arXiv · 2104.13835

Revisiting the representation theorem of finite distributive lattices with principal congruences

G. Grätzer·H. Lakser
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Abstract

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.~Gr\"atzer 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.

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G. Grätzer, H. Lakser. 2021-04-28. Revisiting the representation theorem of finite distributive lattices with principal congruences. https://arxiv.org/abs/2104.13835

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