Strongly regular relations on regular hypergroups

Ameri, Reza; Afshar, Behnam

doi:10.22103/jmmr.2024.23228.1612

Strongly regular relations on regular hypergroups

Document Type : Research Paper

Authors

Reza Ameri

Behnam Afshar

Department of Mathematics, Statistics and Computer Science, University of Tehran, Tehran, Iran.

10.22103/jmmr.2024.23228.1612

Abstract

Hypergroups that have at least one identity element and where each element has at least one inverse are called regular hypergroup. In this regards, for a regular hypergroup $H$, it is shown that there exists a correspondence between the set of all strongly regular relations on $H$ and the set of all normal subhypergroups of $H$ containing $S_{\beta}$. More precisely, it has been proven that for every strongly regular relation $\rho$ on $H$, there exists a unique normal subhypergroup of $H$ containing $S_{\beta}$, such that its quotient is a group, isomorphic to $H/\rho$. Furthermore, this correspondence is extended to a lattice isomorphism between them.

Keywords

Normal subhypergroup

Regular hypergroup

Strongly regular relation

Subjects

Algebra

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