Semilattice relations on a semihypergroup

Ze Gu; Ze Gu

doi:10.3934/math.2023758

AIMS Mathematics

2023, Volume 8, Issue 6: 14842-14849. doi: 10.3934/math.2023758

Previous Article Next Article

Research article Special Issues

Semilattice relations on a semihypergroup

Ze Gu ^,

School of Mathematics and Statistics, Zhaoqing University, Zhaoqing, Guangdong, China

Received: 22 February 2023 Revised: 12 April 2023 Accepted: 14 April 2023 Published: 21 April 2023
MSC : 06B23, 20M10, 20N20

In this paper, we give a unified method for constructing commutative relations, band relations and semilattice relations on a semihypergroup. Moreover, we show that the set of all commutative relations, the set of all band relations and the set of all semilattice relations on a semihypergroup are complete lattices.
- semihypergroup,
- commutative relation,
- band relation,
- semilattice relation,
- complete lattice
Citation: Ze Gu. Semilattice relations on a semihypergroup[J]. AIMS Mathematics, 2023, 8(6): 14842-14849. doi: 10.3934/math.2023758

Related Papers:

Abstract

In this paper, we give a unified method for constructing commutative relations, band relations and semilattice relations on a semihypergroup. Moreover, we show that the set of all commutative relations, the set of all band relations and the set of all semilattice relations on a semihypergroup are complete lattices.

References

[1]	B. Davvaz, Semihypergroup Theory, London: Academic Press, 2016. https://doi.org/10.1016/C2015-0-06681-3
[2]	M. De Salvo, D. Fasino, D. Freni, G. Lo Faro, $1$-hypergroups of small sizes, Mathematics, 9 (2021), 108. https://doi.org/10.3390/math9020108 doi: 10.3390/math9020108
[3]	M. De Salvo, D. Fasino, D. Freni, G. Lo Faro, On hypergroups with a $\beta$-class of finite height, Symmetry, 12 (2020), 168. https://doi.org/10.3390/sym12010168 doi: 10.3390/sym12010168
[4]	M. Koskas, Groupoides, demi-hypergroupes et hypergroupes, J. Math. Pures Appl., 49 (1970), 155–192.
[5]	D. Freni, A new characterization of the derived hypergroup via strongly regular equivalences, Comm. Algebra, 30 (2006), 3977–3989. https://doi.org/10.1081/AGB-120005830 doi: 10.1081/AGB-120005830
[6]	H. Aghabozorgi, B. Davvaz, M. Jafarpour, Nilpotent groups derived from hypergroups, J. Algebra, 382 (2013), 177–184. https://doi.org/10.1016/j.jalgebra.2013.02.011 doi: 10.1016/j.jalgebra.2013.02.011
[7]	R. Ameri, E. Mohammadzadeh, Engel groups derived from hypergroups, European J. Combin., 44 (2015), 191–197. https://doi.org/10.1016/j.ejc.2014.08.004 doi: 10.1016/j.ejc.2014.08.004
[8]	Z. Gu, On cyclic hypergroups, J. Algebra Appl., 18 (2019), 1950213. https://doi.org/10.1142/S021949881950213X doi: 10.1142/S021949881950213X
[9]	Z. Gu, X. L. Tang, Ordered regular equivalence relations on ordered semihypergroups, J. Algebra, 450 (2016), 384–397. https://doi.org/10.1016/j.jalgebra.2015.11.026 doi: 10.1016/j.jalgebra.2015.11.026
[10]	M. Jafarpour, H. Aghabozorgi, B. Davvaz, Solvable groups derived from hypergroups, J. Algebra Appl., 15 (2016), 1650067. https://doi.org/10.1142/S0219498816500675 doi: 10.1142/S0219498816500675
[11]	S. S. Mousavi, V. Leoreanu-Fotea, M. Jafarpour, H. Babaei, Equivalence relations in semihypergroups and the corresponding quotient structures, European J. Combin., 33 (2012), 463–473. https://doi.org/10.1016/j.ejc.2011.11.008 doi: 10.1016/j.ejc.2011.11.008
[12]	T. S. Blyth, Lattices and Ordered Algebraic Structures, London: Springer, 2005. https://doi.org/10.1007/b139095
[13]	R. Ameri, Fuzzy congruence of hypergroups, J. Intell. Fuzzy Syst., 19 (2008), 141–149. https://doi.org/10.5555/1369389.1369394 doi: 10.5555/1369389.1369394

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)