A novel approach to study ternary semihypergroups in terms of prime soft hyperideals

Shahida Bashir; Rabia Mazhar; Bander Almutairi; Nauman Riaz Chaudhry; Shahida Bashir; Rabia Mazhar; Bander Almutairi; Nauman Riaz Chaudhry

doi:10.3934/math.20231033

AIMS Mathematics

2023, Volume 8, Issue 9: 20269-20282. doi: 10.3934/math.20231033

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A novel approach to study ternary semihypergroups in terms of prime soft hyperideals

1.
Department of Mathematics, University of Gujrat, Gujrat 50700, Pakistan
2.
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455 Riyadh 11451, Saudi Arabia
3.
Department of Computer Science, University of Gujrat, Gujrat 50700, Pakistan

Received: 27 April 2023 Revised: 04 June 2023 Accepted: 09 June 2023 Published: 20 June 2023
MSC : 20N10, 18B40

In this paper, we give the generalized form of soft semihypergroups in ternary structure and have studied it with the help of examples. There are some structures that are not appropriately handled by using the binary operation of the semihypergroup, such as all the sets of non-positive numbers are not closed under binary operation but hold for ternary operation. To deal with this type of problem and handling special type of uncertainty, we study the ternary semihypergroup in terms of prime soft hyperideals. We have introduced prime, strongly prime, semiprime, irreducible and strongly irreducible soft bi-hyperideals in ternary semihypergroups and studied certain properties of these soft bi-hyperideals in ternary semihypergroups. The main advantage of this paper is that we proved that each soft bi-hyperideal of ternary semihypergroup $K$ is strongly prime if it is idempotent and the set of soft bi-hyperideals of $K$ is totally ordered by inclusion.
Citation: Shahida Bashir, Rabia Mazhar, Bander Almutairi, Nauman Riaz Chaudhry. A novel approach to study ternary semihypergroups in terms of prime soft hyperideals[J]. AIMS Mathematics, 2023, 8(9): 20269-20282. doi: 10.3934/math.20231033

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Abstract

In this paper, we give the generalized form of soft semihypergroups in ternary structure and have studied it with the help of examples. There are some structures that are not appropriately handled by using the binary operation of the semihypergroup, such as all the sets of non-positive numbers are not closed under binary operation but hold for ternary operation. To deal with this type of problem and handling special type of uncertainty, we study the ternary semihypergroup in terms of prime soft hyperideals. We have introduced prime, strongly prime, semiprime, irreducible and strongly irreducible soft bi-hyperideals in ternary semihypergroups and studied certain properties of these soft bi-hyperideals in ternary semihypergroups. The main advantage of this paper is that we proved that each soft bi-hyperideal of ternary semihypergroup $K$ is strongly prime if it is idempotent and the set of soft bi-hyperideals of $K$ is totally ordered by inclusion.

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