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Open Access Research Article

On completely regular 2-duo ordered semihypergroups

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* Corresponding author · click or hover a name for details

pp. 895–908Vol. 44Issue 5July 2023DOI: 10.47974/JIOS-1178XML
Received:
09 Nov 2021
Accepted:
10 May 2022
Published Online:
10 Oct 2023
Article type:
Research Article
Language:
EN
Article no.:
JIOS-1178
Pages:
895–908

Abstract

The concept of duo ordered semihypergroups was introduced by Ardekani and Davvaz in 2018. In this paper, we introduce the concept of n-duo ordered semihypergroups. We show that every duo ordered semihypergroup is an n-duo ordered semihypergroup (n ≥ 2),  but the converse is not generally true. We investigate the concept of completely regular 2-duo ordered semihypergroups and give their characterizations in terms of (2, 0) -hyperideals, (0, 2) -hyperideals, (2, 2) -hyperideals and (2, 2) -quasi-hyperideals. Finally, we show that in 2-duo ordered semihypergroups, every (2, 2) -hyperideal is quasi-prime. 

Keywords

Subject Classifications

(2010) 20N2020N99

References

[1] L. K. Ardekani and B. Davvaz, Ordered semihypergroup constructions, Bol. Mat. 25(2) (2018), 77-99.
[2] M. Azhar, M. Gulistan, N. Yaqoob N and S. Kadry, On fuzzy ordered LA-semihypergroups, Int. J. Analy. Appl., 16(2) (2018), 276-289.
[3] T. Changphas and B. Davvaz, Properties of hyperideals in ordered semihypergroups, Ital. J. Pure Appl. Math. 33 (2014), 425-432.
[4] T. Changphas and B. Davvaz, Bi-hyperdeals and quasi-hyperideals in ordered semihypergroups, Ital. J. Pure Appl. Math. 35 (2015), 493-508.
[5] M. Farooq, A. Khan and M. Izhar, Characterizations of ordered semihypergroups vai-int-soft bi-hyperideals, Algebr. Struct. Appl. 8(2) (2021), 157-175.
[6] Z. Gu, J. Tang and X. Xie, A further study on hyperideals of ordered semihypergroups, Ital. J. Pure Appl. Math. 40 (2020), 692-698.
[7] D. Heidari and B. Davvaz, On ordered hyperstructures, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 73(2) (2011), 85-96.
[8] N. Kehayopulu, On regular, regular duo ordered semigroups, Pure Math. Appl. 5(3) (1994), 161-176.
[9] M. Khau, F. Smarandache and T. Aziz, Fuzzy abel grassmann groupoids, The Educational Publisher inc, (2015).
[10] P. Luangchaisri and T. Changphas, On completely regular 2-duo semigroups, Quasigroups Relat. Syst. 29 (2021), 89-96.
[11] G. Madhavi, A. Behzadi and A. Taghavi, Ordered hypervector spaces, Italian J. Pure Appl. Math., 44 (2020), 687-697.
[12] A. Mahboob, N. M. Khan and B. Davvaz, Structural properties for -quasi-hyperideals in ordered semihypergroups, Tbilisi Math. J. 11(4) (2018), 145-163.
[13] A. Mahboob, N. M. Khan and B. Davvaz, -Hyperideals in ordered semihypergroups, Categ. Gen. Algebr. Struct. Appl. 12(1) (2020), 43-67.
[14] F. Marty, Sur une generalization de la notion de groupe, 8th Congres Math. Scandinaves, Stockholm (1934), 45-49.
[15] B. Pibaljommee and B. Davvaz, Characterizations of (fuzzy) bi-hyperideals in ordered semihypergroups, J. Intell. Fuzzy Syst. 28 (2015), 2141-2148, DOI: 10.3233/IFS-141494.
[16] S. Suebsung, W. Yonthanthum, K. Hila and R. Chinram, On almost quasi-hyperideals in semihypergroups, J. Discrete Math. Sci. Crypt, 24(1) (2021), 235-244, DOI: 10.1080/09720529.2020.1826167.
[17] A. F. Talee, M. Y. Abbasi, S. A. Khan and K. Hila, Fuzzy set approach to hyperideal theory of po-ternary semihypergroups, J. Discrete Math. Sci. Crypt, 22(3) (2019), 411-431, DOI: 10.1080/09720529.2019.1600846.
[18] J. Tang and B. Davvaz, Study on green’s relation in ordered semihypergroups, Soft Comput., 24 (2020), 11189-11197, DOI: 10.1007/s00500-020-05035-y.
[19] J. Tang, B. Davvaz and X. Xie, A study on (fuzzy) quasi--hyperideal in ordered -semihypergroups, J. Int. Fuzzy Syst. 32(6) (2017), 3821-3838, DOI: 10.3233/IFS-162117.
[20] J. Tang and N. Yaqoob, A novel investigation on fuzzy hyperidealin ordered *-semihypergroups, Comput. Appl. Math., 40 (2021), Article Number 43, DOI: 10.1007/s40314-020-01388-0.
[21] P. Yiarayong, B. Davvaz and R. Chinram, On right chain ordered semihypergroups, J. Math. Comput. Sci. 24 (2022), 59-72.

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