On enumeration and classification of $EL^2$-semihypergroups and $EL^2$-$H_v$-semihypergroups with 2 elements

Document Type : Research Paper

Authors

1 Department of Mathematics, Payame Noor University, P.O.BOX 19395-3697 Tehran, Iran,

2 Department of Mathematics, Shahid Ashrafi Esfahani University, Isfahan, Iran

3 Technical and Vocational University(TVU), Tehran, Iran

Abstract

$EL$-hypergroups were defined by Chvalina 1995. Till
now, no exact statistics of $EL$-hypergroups have been done.\\ Moreover, there is no classification of $EL$-hypergroups and $EL^2$-hypergroups even over small sets.
In this paper, we classify all $EL$-(semi)hypergroups over sets with
two elements obtained from quasi ordered semigroups. Also, we characterize all quasi ordered $H_v$-group and then we enumerate the number of $EL^2$-$H_v$-hypergroups and $EL^2$-hypergroups of order 2.

Keywords

Journal of Algebra and Related Topics
Volume 11, Issue 2
December 2023
Pages 85-97

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