Representations of n-cyclic groupoids
type: Item
instance of: scholarly article
title: Representations of n-cyclic groupoids
zbMATH Open document ID: 0669.20058
DOI: 10.1007/BF01243869
author: Anna Romanowska
author: B. Roszkowska
published in: Algebra Universalis
publication date: 1989-01-01T00:00:00Z
review text: An n-cyclic groupoid is a groupoid satisfying the following four identities: \((xy)z=(xz)y\), \(xx=x\), \(x(yz)=xy\), \((((xy)y)...)y=x\) where y is repeated n times. A decomposition of an n-cyclic groupoid into a disjoint sum of abelian groups is found and the result is applied to describe free objects, to establish properties of congruence relations and to characterize subdirectly irreducible groupoids in the variety of n-cyclic groupoids.
Mathematics Subject Classification ID: 20N99
Mathematics Subject Classification ID: 08A05
zbMATH DE Number: 4095792
zbMATH Keywords: identities
zbMATH Keywords: disjoint sum of abelian groups
zbMATH Keywords: free objects
zbMATH Keywords: congruence relations
zbMATH Keywords: subdirectly irreducible groupoids
zbMATH Keywords: variety of n-cyclic groupoids
reviewed by: Jaroslav Ježek
MaRDI profile type: Publication
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cites work: Homomorphisms and subdirect decompositions of semigroups
description: scientific article; zbMATH DE number 4095792