Bi-Hyperideals in Ternary Semihypergroups (original) (raw)

On Minimal and Maximal Hyperidealsin n-ary Semihypergroups

Mathematics

The concept of j-hyperideals, for all positive integers 1≤j≤n and n≥2, in n-ary semihypergroups, is a generalization of the concept of left, lateral and right hyperideals in ternary semihypergroups. In this paper, we first introduce the concept of j-(0-)simple n-ary semihypergroups and discuss their related properties through terms of j-hyperideals. Furthermore, we characterize the minimality and maximality of j-hyperideals in n-ary semihypergroups and establish the relationships between the (0-)minimal, maximal j-hyperideals and the j-(0-)simple n-ary semihypergroups. Our main results are to extend and generalize the results on semihypergroups and ternary semihypergroups. Moreover, a related question raised by Petchkaew and Chinram is solved.

Semihypergroups associated with ternary relations

Afrika Matematika, 2018

Davvaz and Leoreanu-Fotea (Commun Algebra 38(10):3621-3636, 2010) studied binary relations on ternary semihypergroups. A ternary relation or triadic relation is a relation in which the number of places in the relation is three. Now, in this paper, instead of binary relations we consider ternary relations and instead of ternary semihypergroups we consider ordinary semihypergroups. Then, we study ternary relations on semihypergroups. In particular, we discuss some properties of compatible ternary relations on them.

Pseudosymmetric hyperideals in ternary semi hypergroups

ESSENCE OF MATHEMATICS IN ENGINEERING APPLICATIONS: EMEA-2020, 2021

In this paper we introduce pseudosymmetric hyperideals of a ternary semi hypergroup. We also study some properties of principal hyperideal; completely semiprime hyperideal of a TSHG and characterized them. The interrelation among them is examined in ternary semi hypergroups extending the related results from semigroups.

(2005-1005) Characterization of ordered semihypergroups in terms of uni-soft bi-hyperideals

2020

In this paper, we introduce the concept of unionsoft (briefly, uni-soft) bi-hyperideal of an ordered semihypergroup. The notions of prime (strongly prime, semiprime, irreducible, and strongly irreducible) uni-soft bi-hyperideals in ordered semihypergroups are introduced and related properties are investigated. Numerous examples of these notions are given. The relationship between prime and strongly prime, irreducible and strongly irreducible uni-soft bi-hyperideals are considered and characterizations of these concepts are established. Regular and intra-regular ordered semihypergroups are characterized in terms of these notions.

Characterization of ordered semihypergroups in terms of uni-soft bi-hyperideals

Journal of Algebraic Hyperstructures and Logical Algebras, 1999

A new approach towards int-soft hyperideals in ordered ternary semihypergroups

Journal of Discrete Mathematical Sciences and Cryptography, 2020

This paper deals with a class of algebraic hyperstructures called ordered ternary semihypergroups which are studied in terms of int-soft hyperideals. We introduce the notion of int-soft hyperideals in ordered ternary semihypergroups and investigate some properties of them. We also introduce the concepts of convex soft sets and int-soft points and discuss their properties. Moreover, the classes of regular and intra-regular ordered ternary semihpergroups are characterized in terms of int-soft hyperideals.

On Some Hyperideals in Ordered Semihypergroups

Abul Basar, Shahnawaz Ali, M Y Abbasi, Bhavanari Satyanarayana, Poonam Kumar Sharma, Journal of New Theory, 29, 42-48, 2019

In this paper, we study ordered hyperideals in ordered semihypergroups. Also, we study (m, n)-regular ordered semihypergroups in terms of ordered (m, n)-hyperideals. Furthermore, we obtain some ideal theoretic results in ordered semihypergroups.

Special Types of Ternary Semigroups V . Jyothi

2014

The main goal of this paper is to initiate the notions of U-ternarysemigroup and V-ternary semigroup in the class of orbitary ternarysemigroups. We study prime ideals and maximal ideals in a Uternarysemigroup and characterize V-ternary semigroup. It is proved that if T is a globally idempotent ternarysemigroups with maximal ideal, then either T is a V-ternarysemigroup or T has a unique maximal ideal which is prime. Finally we proved that a ternarysemigroup T is a V-ternarysemigroup if and only if T has atleast one proper prime ideal and if { } is the family of all proper prime ideals, then < x > =T for x T\U or T is a simple ternarysemigroup.

Special Types of Ternary Semigroups

2015

Abstract: The main goal of this paper is to initiate the notions of U-ternarysemigroup and V-ternary semigroup in the class of orbitary ternarysemigroups. We study prime ideals and maximal ideals in a U-ternarysemigroup and characterize V-ternary semigroup. It is proved that if T is a globally idempotent ternarysemigroups with maximal ideal, then either T is a V-ternarysemigroup or T has a unique maximal ideal which is prime. Finally we proved that a ternarysemigroup T is a V-ternarysemigroup if and only if T has atleast one proper prime ideal and if { } is the family of all proper prime ideals, then < x> =T for x T\U or T is a simple ternarysemigroup.

$(m,n)$-Hyperideals in Ordered Semihypergroups

Categories and General Algebraic Structures with Application

In this paper, first we introduce the notions of an (m, n)hyperideal and a generalized (m, n)-hyperideal in an ordered semihypergroup, and then, some properties of these hyperideals are studied. Thereafter, we characterize (m, n)-regularity, (m, 0)-regularity, and (0, n)-regularity of an ordered semihypergroup in terms of its (m, n)-hyperideals, (m, 0)-hyperideals and (0, n)-hyperideals, respectively. The relations mI , In, H n m , and B n m on an ordered semihypergroup are, then, introduced. We prove that B n m ⊆ H n m on an ordered semihypergroup and provide a condition under which equality holds in the above inclusion. We also show that the (m, 0)-regularity [(0, n)regularity] of an element induce the (m, 0)-regularity [(0, n)-regularity] of the whole H n m-class containing that element as well as the fact that (m, n)regularity and (m, n)-right weakly regularity of an element induce the (m, n)regularity and (m, n)-right weakly regularity of the whole B n m-class and H n mclass containing that element, respectively.