Strongly regular relations on regular hypergroups

Document Type : Research Paper

Authors

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

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.

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References

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History

  • Receive Date: 12 April 2024
  • Revise Date: 28 June 2024
  • Accept Date: 07 August 2024

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