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September 2018 Structural properties for $(m,n)$-quasi-hyperideals in ordered semihypergroups
Ahsan Mahboob, Noor Mohammad Khan, Bijan Davvaz
Tbilisi Math. J. 11(4): 145-163 (September 2018). DOI: 10.32513/tbilisi/1546570891

Abstract

In this paper, we first introduce the notion of an $(m,n)$-quasi-hyperideal in an ordered semihypergroup and, then, study some properties of $(m,n)$-quasi-hyperideals for any positive integers $m$ and $n$. Thereafter, we characterize the minimality of an $(m,n)$-quasi-hyperideal in terms of $(m,0)$-hyperideals and $(0,n)$-hyperideals respectively. The relation $\mathcal{Q}_m^n$ on an ordered semihypergroup is, then, introduced for any positive integers $m$ and $n$ and proved that the relation $\mathcal{Q}_m^n$ is contained in the relation $\mathcal{Q}=\mathcal{Q}_1^1$. We also show that, in an $(m,n)$-regular ordered semihypergroup, the relation $\mathcal{Q}_m^n$ coincides with the relation $\mathcal{Q}$. Finally, the notion of an $(m,n)$-quasi-hypersimple ordered semihypergroup is introduced and some properties of $(m,n)$-quasi-hypersimple ordered semihypergroups are studied. We further show that, on any $(m,n)$-quasi-hypersimple ordered semihypergroup, the relations $\mathcal{Q}_m^n$ and $\mathcal{Q}$ are equal and are universal relations.

Citation

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Ahsan Mahboob. Noor Mohammad Khan. Bijan Davvaz. "Structural properties for $(m,n)$-quasi-hyperideals in ordered semihypergroups." Tbilisi Math. J. 11 (4) 145 - 163, September 2018. https://doi.org/10.32513/tbilisi/1546570891

Information

Received: 6 June 2018; Accepted: 8 October 2018; Published: September 2018
First available in Project Euclid: 4 January 2019

zbMATH: 07172294
MathSciNet: MR3954213
Digital Object Identifier: 10.32513/tbilisi/1546570891

Subjects:
Primary: 20N20

Rights: Copyright © 2018 Tbilisi Centre for Mathematical Sciences

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Vol.11 • No. 4 • September 2018
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