Distributive groupoids and symmetry-by-mediality
type: Item
instance of: scholarly article
title: Distributive groupoids and symmetry-by-mediality
zbMATH Open document ID: 0552.20048
DOI: 10.1007/BF01190430
published in: Algebra Universalis
publication date: 1984-01-01T00:00:00Z
review text: It is proved that every distributive idempotent groupoid \(G\) is symmetric-by-medial, i.e. there exists a congruence \(\rho\) of \(G\) such that \(G/\rho\) is symmetric and every block of \(\rho\) is a medial subgroupoid of \(G\). This result has several important consequences. One of them: every free distributive groupoid is cancellative.
Mathematics Subject Classification ID: 20N05
Mathematics Subject Classification ID: 08A30
zbMATH DE Number: 3879170
zbMATH Keywords: distributive idempotent groupoids
zbMATH Keywords: congruences
zbMATH Keywords: medial subgroupoids
zbMATH Keywords: free distributive groupoids
author: Jaroslav Ježek
author: Tomáš Kepka
reviewed by: Vladimir Fleischer
MaRDI profile type: Publication
cites work: On convex linear forms
cites work: Distributive groupoids and the finite basis property
cites work: Every distributive groupoid is trimedial
cites work: Étude algébrique de la notion de moyenne
full work available at URL: https://doi.org/10.1007/bf01190430
OpenAlex ID: W2046104457
description: scientific article; zbMATH DE number 3879170