Hypergroups and binary relations
type: Item
instance of: scholarly article
title: Hypergroups and binary relations
zbMATH Open document ID: 1016.20056
author: P. Corsini
author: Violeta Leoreanu
published in: Algebra Universalis
publication date: 2003-04-23T00:00:00Z
review text: A hypergroupoid is a set \(H\neq\emptyset\) endowed with a function \(\circ\) from \(H\times H\) to the set of non-empty subsets of \(H\). A hypergroup is a hypergroupoid \((H,\circ)\) such that \(x\circ(y\circ z)=(x\circ y)\circ z\) and \(x\circ H=H=H\circ x\) for all \(x,y,z\in H\). To a binary relation \(R\) on \(H\), a hypergroupoid \(H_R\) is associated as follows: \(x\circ x=\{y\in H;\;(x,y)\in R\}\) and \(x\circ y=x\circ x\cup y\circ y\). I. G. Rosenberg found conditions on \(R\) such that \(H_R\) is a hypergroup. The first author studied these hypergroups under the union, intersection, Cartesian product, product and direct limit of relations. In this paper this treatment is continued. The authors obtain several results for which mutual associativity plays a role and describe hypergroups associated with trees.
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 20N20
zbMATH DE Number: 1899942
zbMATH Keywords: hypergroups
zbMATH Keywords: hypergroupoids
zbMATH Keywords: binary relations
zbMATH Keywords: associativity
MaRDI profile type: Publication
full work available at URL: s000120050162
OpenAlex ID: W1997976470
DOI: 10.1007/S000120050162
description: scientific article; zbMATH DE number 1899942