About the fundamental relations defined on the hypergroupoids associated with binary relations.
type: Item
instance of: scholarly article
title: About the fundamental relations defined on the hypergroupoids associated with binary relations.
zbMATH Open document ID: 1209.20073
author: Irina Cristea
author: Mirela Ştefănescu
author: Carmen Angheluţă
published in: European Journal of Combinatorics
publication date: 2010-11-22T00:00:00Z
review text: The paper deals with connections between hypergroupoids and \(n\)-ary relations. The authors show that the hypergroupoid associated with an \(n\)-ary relation [as in \textit{I. G. Rosenberg}, Ital. J. Pure Appl. Math. 4, 93-101 (1998; Zbl 0962.20055), or \textit{P. Corsini}, Ital. J. Pure Appl. Math. 7, 11-18 (2000; Zbl 0972.20042), or \textit{I. Cristea, M. Ştefănescu}, Eur. J. Comb. 31, No. 3, 780-789 (2010; Zbl 1194.20068)], coincides with the one associated with a certain induced binary relation. On the basis of the properties of some fundamental relations defined on a hypergroupoid, they determine necessary and sufficient conditions for two elements in a hypergroupoid associated with a binary relation to be operationally equivalent or inseparable. They present some links with the Boolean matrices associated with binary relations and determine conditions for a Boolean matrix \(M(\rho)\) in order to have that the hypergroupoid associated with \(\rho\) is a reduced hypergroup. Also, they characterize the matrix representing a binary relation such that its associated hypergroupoid is an \(H_v\)-group.
reviewed by: Bijan Davvaz
Mathematics Subject Classification ID: 20N20
Mathematics Subject Classification ID: 20N15
Mathematics Subject Classification ID: 08A30
zbMATH DE Number: 5817919
zbMATH Keywords: hypergroupoids
zbMATH Keywords: hypergroups
zbMATH Keywords: \(H_v\)-groups
zbMATH Keywords: \(n\)-ary relations
zbMATH Keywords: binary relations
zbMATH Keywords: fundamental relations
describes a project that uses: BinaryTest
MaRDI profile type: Publication
full work available at URL: j.ejc.2010.07.013
OpenAlex ID: W2145396599
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DOI: 10.1016/J.EJC.2010.07.013
description: scientific article; zbMATH DE number 5817919