Representing homomorphisms of distributive lattices as restrictions of congruences of rectangular lattices
type: Item
instance of: scholarly article
title: Representing homomorphisms of distributive lattices as restrictions of congruences of rectangular lattices
zbMATH Open document ID: 1269.06004
author: Gábor Czédli
published in: Algebra Universalis
publication date: 2012-09-27T00:00:00Z
review text: This paper is the newest contribution to the problem of representing finite distributive lattices as congruence lattices of lattices with special properties. The results are mostly of technical character and are prompting alternative proofs of known theorems (cf. [\textit{G. Grätzer} and \textit{E. Knapp}, Acta Sci. Math. 75, No. 1--2, 29--48 (2009; Zbl 1199.06029); \textit{E. T. Schmidt}, Acta Sci. Math. 77, No. 1--2, 47--52 (2011; Zbl 1249.06022)]. We can present a typical example: Every finite nontrivial distributive lattice \(D\) is isomorphic to the congruence lattice of a rectangular lattice. (Recall that a finite lattice \(M\) is called rectangular, if \(M\) is planar, semimodular, \(|M|\geq 3\), and there exists only one couple \(a, b\in M-\{0,1\}\) of double-irreducible elements such that \(a\) is the left weak corner and \(b\) is the right weak corner of \(M,\) respectively, and both elements are complementary in \(M.\))
Mathematics Subject Classification ID: 06D05
Mathematics Subject Classification ID: 06B10
Mathematics Subject Classification ID: 06C10
zbMATH DE Number: 6087533
zbMATH Keywords: distributive lattice
zbMATH Keywords: quasiordering
zbMATH Keywords: semimodular lattice
zbMATH Keywords: slim lattice
zbMATH Keywords: rectangular lattice
zbMATH Keywords: congruence lattice
reviewed by: Tibor Katriňák
MaRDI profile type: Publication
full work available at URL: s00012-012-0190-3
OpenAlex ID: W1977147413
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DOI: 10.1007/S00012-012-0190-3
description: scientific article; zbMATH DE number 6087533