2-uniform congruences in majority algebras and a closure operator
type: Item
instance of: scholarly article
title: 2-uniform congruences in majority algebras and a closure operator
zbMATH Open document ID: 1121.08002
published in: Algebra Universalis
publication date: 2007-09-03T00:00:00Z
review text: A congruence \(\alpha \) of a finite algebra is called uniform if all its classes have the same number of elements (if all the \(\alpha\)-classes are two-element then \(\alpha \) is said to be a \(2\)-uniform congruence). If all congruences of \(A\) are uniform then \(A\) is said to be a uniform algebra. In [Acta Sci. Math. 71, No. 3--4, 457--460 (2005; Zbl 1101.06004)], \textit{K. Kaarli} proved that uniform finite lattices are congruence permutable. The main result of the present paper is in connection with the result of Kaarli: For every finite algebra \(A\) with a majority term any two \(2\)-uniform congruences of \(A\) permute.
Mathematics Subject Classification ID: 08A30
Mathematics Subject Classification ID: 06A15
zbMATH DE Number: 5186251
zbMATH Keywords: Galois connection
zbMATH Keywords: closure operator
zbMATH Keywords: majority term
zbMATH Keywords: near-unanimity term
zbMATH Keywords: uniform congruence
zbMATH Keywords: 2-uniform congruence
zbMATH Keywords: concept lattice
zbMATH Keywords: association rule
author: Gábor Czédli
reviewed by: Dimitru Buşneag
MaRDI profile type: Publication
full work available at URL: s00012-007-2021-5
OpenAlex ID: W1980400028
DOI: 10.1007/S00012-007-2021-5
description: scientific article; zbMATH DE number 5186251