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A study of ordered quasi-hyperideals and ordered bi-hyperideals in regular ordered semihypergoups

Department of Natural and Applied Sciences, Glocal University, Mirzapur, Saharanpur, U. P., India.

Department of Mathematics, Jamia Millia Islamia, New Delhi, India.

* Corresponding Author
Annals of Communications in Mathematics 2021
, 4 (3),
293-306.
https://doi.org/10.62072/acm.2021.040309
Received: 20 November 2021 |
Accepted: 27 December 2021 |
Published: 31 December 2021

Abstract

In this paper, we introduce the concept of ordered quasi-hyperideals of regular ordered semihypergroups, and study the basic results on ordered quasi-hyperideals of ordered semihypergroups. We also investigate regular ordered semihypergroups in terms of its ordered quasi-hyperideals, ordered right hyperideals and ordered left hyperideals. We prove that: (i) A partially ordered semihypergroup S is regular if and only if for every ordered bi-hyperideal B, every ordered hyperideal I and every ordered quasi-hyperideal Q, we have B ∩ I ∩ Q ⊆ (B ◦ I ◦ Q], and (ii) A partially ordered semihypergroup S is regular if and only if for every ordered quasi-hyperideal Q, every ordered left hyperideal L and every ordered right-hyperideal R, we have R ∩ Q ∩ L ⊆ (R ◦ Q ◦ L].

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Cite This Article

A study of ordered quasi-hyperideals and ordered bi-hyperideals in regular ordered semihypergoups.

Annals of Communications in Mathematics,

2021,
4 (3):
293-306.
https://doi.org/10.62072/acm.2021.040309
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  • Copyright (c) 2023 by the Author(s). Licensee Techno Sky Publications. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

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