Graphical algebras -- a new approach to congruence lattices
type: Item
instance of: scholarly article
title: Graphical algebras -- a new approach to congruence lattices
zbMATH Open document ID: 1221.08001
author: Toby Kenney
published in: Algebra Universalis
publication date: 2011-05-11T00:00:00Z
review text: A graphical algebra is a complete lattice together with some special mapping which generalizes the graphical composition introduced by \textit{H.Werner} [Colloq. Math. Soc. Janos Bolyai 14, 433--453 (1976; Zbl 0363.06002)]. Both the abstract characterization as well as one based on some special class of graphs are given and studied in full detail. The main result is the finding of sufficient conditions for a graphical algebra to be a congruence graphical algebra. As a corollary the author obtains the well-known result that any algebraic lattice is the congruence lattice of an algebra [\textit{G. Grätzer} and \textit{E. T. Schmidt}, Acta Sci. Math. 24, 34--50 (1963; Zbl 0117.26101)]. An extensive list of open problems concludes the paper.
reviewed by: Anna Zamojska-Dzienio
Mathematics Subject Classification ID: 08A30
Mathematics Subject Classification ID: 06B15
zbMATH DE Number: 5886738
zbMATH Keywords: congruence lattice
zbMATH Keywords: graphical algebra
zbMATH Keywords: graphical composition
MaRDI profile type: Publication
full work available at URL: s00012-011-0105-8
OpenAlex ID: W2077685336
cites work: Q5727672
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DOI: 10.1007/S00012-011-0105-8
description: scientific article; zbMATH DE number 5886738