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, India2Department of Mathematics, Millat College, a Constituent Unit of L. N. Mithila University, Bibi Pakar, Darbhanga, Bihar, 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/).