Strongly regular relations on regular hypergroups
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...
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| Format: | Article |
| Language: | English |
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Shahid Bahonar University of Kerman
2025-01-01
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| Series: | Journal of Mahani Mathematical Research |
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| Online Access: | https://jmmrc.uk.ac.ir/article_4413_b83319733cedf50f825f1c0f735352a6.pdf |
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| author | Reza Ameri Behnam Afshar |
| author_facet | Reza Ameri Behnam Afshar |
| author_sort | Reza Ameri |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-838e011e857d4676b38b29336ed102dd |
| institution | Kabale University |
| issn | 2251-7952 2645-4505 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Shahid Bahonar University of Kerman |
| record_format | Article |
| series | Journal of Mahani Mathematical Research |
| spelling | doaj-art-838e011e857d4676b38b29336ed102dd2025-01-04T19:30:18ZengShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-79522645-45052025-01-01141738310.22103/jmmr.2024.23228.16124413Strongly regular relations on regular hypergroupsReza Ameri0Behnam Afshar1Department of Mathematics, Statistics and Computer Science, University of Tehran, Tehran, Iran.Department of Mathematics, Statistics and Computer Science, University of Tehran, Tehran, Iran.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.https://jmmrc.uk.ac.ir/article_4413_b83319733cedf50f825f1c0f735352a6.pdfnormal subhypergroupregular hypergroupstrongly regular relation |
| spellingShingle | Reza Ameri Behnam Afshar Strongly regular relations on regular hypergroups Journal of Mahani Mathematical Research normal subhypergroup regular hypergroup strongly regular relation |
| title | Strongly regular relations on regular hypergroups |
| title_full | Strongly regular relations on regular hypergroups |
| title_fullStr | Strongly regular relations on regular hypergroups |
| title_full_unstemmed | Strongly regular relations on regular hypergroups |
| title_short | Strongly regular relations on regular hypergroups |
| title_sort | strongly regular relations on regular hypergroups |
| topic | normal subhypergroup regular hypergroup strongly regular relation |
| url | https://jmmrc.uk.ac.ir/article_4413_b83319733cedf50f825f1c0f735352a6.pdf |
| work_keys_str_mv | AT rezaameri stronglyregularrelationsonregularhypergroups AT behnamafshar stronglyregularrelationsonregularhypergroups |