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Ordered Γ-semihypergroup of the Associated Γ-semihypergroup with All Relative Bi-Γ-hyperideals

Rudauli, Ward Number 11, Block: Bajpatti, Subdivision: Pupri, Sitamarhi, Bihar-843 333, India

Department of Mathematics, Millat College, a Constituent Unit of L. N. Mithila University, Bibi Pakar, Darbhanga, Bihar, India

Department of Mathematics, Jamia Millia Islamia, New Delhi-110 025, India

Department of Mathematics, Acharya Nagarjuna University, Guntur, Andhra Pradesh, India

University Department of Mathematics, L. N. Mithila University, Kameshwaranagar, Darbhanga, Bihar, India

P G Department of Mathematics, D A V College, Jalandhar, Punjab, India

* Corresponding Author
Annals of Communications in Mathematics 2024
, 7 (1),
71-79.
https://doi.org/10.62072/acm.2024.070107
Received: 20 Jan 2024 |
Accepted: 20 Mar 2024 |
Published: 31 Mar 2024

Abstract

In this paper, the main goal is to study an ordered Γ-semihypergroup H in the context of the characterizations of the associated Γ-semihypergroup B(H) of all bi-Γ-hyperideals of H. We show that an ordered Γ-semihypergroup H is a Clifford ordered Γ-semihypergroup if and only if B(H) is a semilattice. We also show that a Γsemihypergroup B(H) is a normal band if and only if the ordered Γ-semihypergroup H is simultaneously regular and intra regular. Furthermore, for each subclass S with many bands, we prove that for an ordered Γ-semihypergroup H, the conditional inclusion B(H) ∈ S holds true.

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Cite This Article

Ordered Γ-semihypergroup of the Associated Γ-semihypergroup with All Relative Bi-Γ-hyperideals.

Annals of Communications in Mathematics,

2024,
7 (1):
71-79.
https://doi.org/10.62072/acm.2024.070107
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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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