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On enumeration of $EL$-hyperstructures with $2$ elements | ||
| Journal of Mahani Mathematical Research | ||
| دوره 11، شماره 1 - شماره پیاپی 21، فروردین 2022، صفحه 145-158 اصل مقاله (463.56 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmrc.2021.18452.1173 | ||
| نویسندگان | ||
| Saeed Mirvakili* 1؛ Sayed Hossein Ghazavi2 | ||
| 1Department of Mathematics, Payame Noor University, Tehran, Iran | ||
| 2Department of Mathematics, University of Shahid Ashrafi Esfahani, P.O.Box 81798-49999, Esfahan, Iran | ||
| چکیده | ||
| $EL$-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 $2$. | ||
| کلیدواژه‌ها | ||
| Ends lemma؛ $EL$-hypergroups؛ $H_v$-group؛ quasi order relation؛ partially order relation | ||
| مراجع | ||
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