relation: http://publicatio.bibl.u-szeged.hu/14522/
title: Characterizing fully principal congruence representable distributive lattices
creator:  Czédli Gábor
description: Motivated by a recent paper of G. Grätzer, a finite distributive lattice D is called fully principal congruence representable if for every subset Q of D containing 0, 1, and the set J(D) of nonzero join-irreducible elements of D, there exists a finite lattice L and an isomorphism from the congruence lattice of L onto D such that Q corresponds to the set of principal congruences of L under this isomorphism. A separate paper of the present author contains a necessary condition of full principal congruence representability: D should be planar with at most one join-reducible coatom. Here we prove that this condition is sufficient. Furthermore, even the automorphism group of L can arbitrarily be stipulated in this case. Also, we generalize a recent result of G. Grätzer on principal congruence representable subsets of a distributive lattice whose top element is join-irreducible by proving that the automorphism group of the lattice we construct can be arbitrary. © 2018, Springer International Publishing AG, part of Springer Nature.
date: 2018
type: Folyóiratcikk
type: PeerReviewed
format: text
identifier: http://publicatio.bibl.u-szeged.hu/14522/1/czedli_characterizing-fully-principal-congruence-representable-distributive-lattices.pdf
format: text
identifier: http://publicatio.bibl.u-szeged.hu/14522/7/algebra_universlails_79_01_content.pdf
identifier:     Czédli Gábor: Characterizing fully principal congruence representable distributive lattices.   ALGEBRA UNIVERSALIS, 79 (1).   ISSN 0002-5240 (2018)     
identifier: doi:10.1007/s00012-018-0498-8
relation: 3362775
language: eng
relation: info:eu-repo/semantics/altIdentifier/doi/10.1007/s00012-018-0498-8
rights: info:eu-repo/semantics/openAccess