1. bookVolume 41 (2021): Issue 2 (November 2021)
Journal Details
License
Format
Journal
eISSN
2084-0373
First Published
16 Apr 2017
Publication timeframe
2 times per year
Languages
English
access type Open Access

Revisiting the Representation Theorem of Finite Distributive Lattices with Principal Congruences. A Proof-By-Picture Approach

Published Online: 06 Sep 2021
Volume & Issue: Volume 41 (2021) - Issue 2 (November 2021)
Page range: 411 - 417
Received: 14 Jun 2020
Accepted: 31 Oct 2020
Journal Details
License
Format
Journal
eISSN
2084-0373
First Published
16 Apr 2017
Publication timeframe
2 times per year
Languages
English
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. 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

MSC 2010

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