Green's Relations for Hypergroupoids

Authors

DOI:

https://doi.org/10.29020/nybg.ejpam.v11i3.3306

Keywords:

hypergroupoid, right (left) consistent, intra-consistent, congruence, semilattice congruence, right (left) ideal, right (left) simple

Abstract

We give some information concerning the Green's relations $\cal R$ and $\cal L$ in hypergroupoids extending the concepts of right (left) consistent or intra-consistent groupoids in case of hypergroupoids. We prove, for example, that if an hypergroupoid $H$ is right (left) consistent or intra-consistent, then the Green's relations $\cal R$ and $\cal L$ are equivalence relations on $H$ and give some conditions under which in consistent commutative hypergroupoids the relation $\cal R$ (= $\cal L$) is a semilattice congruence. A commutative hypergroupoid is right consistent if and only if it is left consistent and if an hypergroupoid is commutative and right (left) consistent, then it is intra-consistent. A characterization of right (left) consistent (or intra-consistent) right (left) simple hypergroupoids has been also given. Illustrative examples are given.

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Published

2018-07-31

Issue

Section

Computer Science

How to Cite

Green’s Relations for Hypergroupoids. (2018). European Journal of Pure and Applied Mathematics, 11(3), 598-611. https://doi.org/10.29020/nybg.ejpam.v11i3.3306