Monotone clones and congruence modularity
type: Item
instance of: scholarly article
title: Monotone clones and congruence modularity
zbMATH Open document ID: 0711.08008
DOI: 10.1007/BF00346133
published in: Order
publication date: 1990-01-01T00:00:00Z
review text: The scope of this paper is to investigate the relationship between the local shape of an ordered set \({\mathbb{P}}=(P;\leq)\) and the congruence- modularity of the variety \({\mathcal V}\) generated by an algebra \({\mathbb{A}}=(P;F)\) each of whose operations is order-preserving with respect to \({\mathbb{P}}\). Finally a class of ordered sets called braids is introduced and it is shown that if \({\mathbb{P}}\) is a braid of length 1, in particular if \({\mathbb{P}}\) is a crown, then the variety \({\mathcal V}\) is not congruence- modular.
Mathematics Subject Classification ID: 08B10
Mathematics Subject Classification ID: 06A06
Mathematics Subject Classification ID: 08A40
zbMATH DE Number: 4168749
zbMATH Keywords: monotone clone
zbMATH Keywords: local shape of an ordered set
zbMATH Keywords: congruence-modularity
zbMATH Keywords: braids
zbMATH Keywords: crown
author: Brian A. Davey
reviewed by: Dimitru Buşneag
MaRDI profile type: Publication
cites work: Q3934450
cites work: Monotone clones and the varieties they determine
cites work: Q4177625
cites work: Congruence modularity is permutability composed with distributivity
cites work: Semimodular lattices with isomorphic graphs
full work available at URL: https://doi.org/10.1007/bf00346133
OpenAlex ID: W2011106796
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description: scientific article; zbMATH DE number 4168749