Open AccessArticle

On Relative (2, 2)-Γ-hyperideals of 2-duo Ordered Γ-semihypergroups

Abul Basar^1*

Shaista²

Bhavanari Satyanarayana³

Ayaz Ahmad⁴

Poonam Kumar Sharma⁵

and

Mohammad Yahya Abbasi⁶

1Department of Mathematics, Millat College, a Constituent Unit of L. N. Mithila University, Bibi Pakar, Darbhanga, Bihar, India2Rudauli, Ward Number 11, Block: Bajpatti, Subdivision: Pupri, Sitamarhi, Bihar-843 333, India3Department of Mathematics, Acharya Nagarjuna University, Guntur, Andhra Pradesh, India4University Department of Mathematics, L. N. Mithila University, Kameshwaranagar, Darbhanga, Bihar, India5P G Department of Mathematics, D A V College, Jalandhar, Punjab, India6Department of Mathematics, Jamia Millia Islamia, New Delhi-110 025, India

* Corresponding Author: Abul Basar. Email:

Annals of Communications in Mathematics 2024, 7 (1), 47-56. https://doi.org/10.62072/acm.2024.070105

Received: 6 Jan 2024 |

Accepted: 16 Mar 2024 |

Published: 31 Mar 2024

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Abstract

In this paper, first we obtain the necessary and sufficient condition for an ordered Γ-semihypergroup H to be a relative completely regular 2-duo ordered Γ-semihypergroup for any relative (2, 2)-Γ-hyperideal as well as for any relative (2, 2)-quasi-Γ-hyperideal of H. Then, we find the necessary and sufficient condition that Q = (Q2]S for every relative (2, 2)-Γ-hyperideal Q of H to be a relative quasi-Γ-prime with S ⊆ H. Finally, we prove the necessary and sufficient condition for relative (2, 2)-Γ-hyperideal to be a relative quasi-Γ-prime for a relative completely regular and relative (2, 2)-Γ-hyperideal of H making a chain with inclusive relation.

Keywords

(2,2)-quasi-Γ-hyperideal; (2,2)-Γ-hyperideal; 2-duo ordered Γ-semihypergroup; Completely regular ordered Γ-semihypergroup; relative quasi Γ-hyperideal

Cite This Article

Abul Basar, Shaista, Bhavanari Satyanarayana, Ayaz Ahmad, Poonam Kumar Sharma, Mohammad Yahya Abbasi.

On Relative (2, 2)-Γ-hyperideals of 2-duo Ordered Γ-semihypergroups.

Annals of Communications in Mathematics

2024,

7 (1):

47-56.

https://doi.org/10.62072/acm.2024.070105

Copyright © 2024 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/).