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Periodica Mathematica Hungarica

, Volume 69, Issue 1, pp 32–40 | Cite as

An extension theorem for planar semimodular lattices

  • G. Grätzer
  • E. T. SchmidtEmail author
Article

Abstract

We prove that every finite distributive lattice \(D\) can be represented as the congruence lattice of a rectangular lattice \(K\) in which all congruences are principal. We verify this result in a stronger form as an extension theorem.

Keywords

Principal congruence Order Semimodular Rectangular 

Mathematics Subject Classification

Primary 06C10 Secondary 06B10 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ManitobaWinnipegCanada
  2. 2.Mathematical Institute, Budapest University of Technology and EconomicsBudapestHungary

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