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Strongly regular relations on regular hypergroups | ||
| Journal of Mahani Mathematical Research | ||
| دوره 14، شماره 1 - شماره پیاپی 31، فروردین 2025، صفحه 73-83 اصل مقاله (497.98 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2024.23228.1612 | ||
| نویسندگان | ||
| Reza Ameri؛ Behnam Afshar* | ||
| Department of Mathematics, Statistics and Computer Science, University of Tehran, Tehran, Iran. | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Normal subhypergroup؛ Regular hypergroup؛ Strongly regular relation | ||
| مراجع | ||
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[1] Afshar, B., & Ameri, R. (2023). Strongly Regular Relations Derived from Fundamental Relation. Journal of Algebraic Hyperstructures and Logical Algebras, 4(2), 123-130. https://doi.org/10.61838/kman.jahla.4.2.8
[2] Ameri, R., & Rosenberg, I. G. (2009). Congruences of Multialgebras. J. Multiple Valued Log. Soft Comput., 15(5-6), 525-536.
[3] Ameri, R., & Nozari, T. (2010). A new characterization of fundamental relation on hyperrings. Int. J. Contemp. Math. Sci, 5(15), 721-738.
[4] Connes, A., & Consani, C. (2011). The hyperring of adele classes. Journal of Number Theory, 131(2), 159-194. http://doi.org/10.1016/j.jnt.2010.09.001
[5] Connes, A., & Consani, C. (2015). Universal thickening of the eld of real numbers. In Advances in the Theory of Numbers: Proceedings of the Thirteenth Conference of the Canadian Number Theory Association (pp. 11-74). Springer New York. https://doi.org/10.1007/978-1-4939-3201-62
[6] Corsini, P. (1993). Prolegomena of hypergroup theory. Aviani editore.
[7] Corsini, P., & Leoreanu, V. (2013). Applications of hyperstructure theory (Vol. 5). Springer Science & Business Media. http://doi.org/10.1007/978-1-4757-3714-1
[8] Davvaz, B., & Leoreanu-Fotea, V. (2007). Hyperring theory and applications (Vol. 347). International Academic Press, USA.
[9] Davvaz, B., & Leoreanu-Fotea, V. (2022). Hypergroup theory. http://doi.org/10.1142/12645
[10] Freni, D. (2002). A new characterization of the derived hypergroup via strongly regular equivalences. Communications in Algebra, 30(8), 3977-3989. http://doi.org/10.1081/AGB-120005830
[11] Freni, D. (2004). Strongly transitive geometric spaces: Applications to hypergroups and semigroups theory. Taylor & Francis, 969-988. https://doi.org/10.1081/AGB-120027961
[12] Jun, J. U. (2015). Algebraic geometry over semi-structures and hyper-structures of characteristic one (Doctoral dissertation, Johns Hopkins University).
[13] Jun, J. (2018). Algebraic geometry over hyperrings. Advances in Mathematics, 323, 142-192. http://doi.org/10.1016/j.aim.2017.10.043
[14] Koskas, M., & Freni, D. (1970). Groupoids, semi-hypergroups and hypergroups. Journal de Mathematiques Pures et Appliquees, 155.
[15] Marty, F. (1934). Sur une generalization de la notion de groups. In 8th congress Math. Scandinaves, Stockholm,(1934).
[16] Vougiouklis, T. (1991, April). The fundamental relation in hyperrings. The general hyper eld. In Proc. Fourth Int. Congress on Algebraic Hyperstructures and Applications (AHA 1990), World Scienti c (pp. 203-211). | ||
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