Some Properties of Relative Bi-(Int-)Γ-Hyperideals in Ordered Γ-Semihypergroups

Abstract

In this article, we study the concept of relative bi-Γ-hyperideals (J-bi-Γ-hyperideals) in ordered Γ-semihypergroups and present some related examples of this concept. Especially, characterization of J-simple ordered Γ-semihypergroups in terms of J-bi-Γ-hyperideals is given. Furthermore, we define the notion of J-(bi-)int-Γ-hyperideals in ordered Γ-semihypergroups and investigate its related properties. We show that J-int-Γ-hyperideals and J-Γ-hyperideals coincide in a J-regular ordered Γ-semihypergroup.

A Note on the w-Pseudo-Orders in Ordered (Semi)Hyperrings

“…Ordered structures have applications in various fields, such as computer science, physics, coding theory and topological spaces, etc. Omidi and Davvaz in [10][11][12] and Rao et al in [13][14][15] obtained some results on ordered hyperstructures connected with pseudo-orders and k-hyperideals.…”

A Study onA−I−Γ-Hyperideals andm,n−Γ-Hyperfilters in OrderedΓ-Semihypergroups

“…Recently, fuzzy set theory has been well developed in the framework of ordered Γ-semihypergroup theory [19]. In 2020, Rao et al [20] introduced and studied the concept of relative bi-(int-)Γ-hyperideals in ordered Γ-semihypergroups. e beauty of relative bi-(int-)Γ-hyperideals is that instead of involving all the elements of the ordered Γ-semihypergroup S, we deal with the elements belonging to the nonempty subsets of S. e concept of A-ideals of semigroups was introduced by Grosek and Satko [21] and was further investigated in [22].…”

A Note on the Connection between Ordered Semihyperrings

“…In [21], Cristea and Kankaraš studied the reducibility of hyperrings. In [22,23], the (m-)k-hyperideals of an ordered semihyperring are studied. In [23], the concept of derivation on ordered semihyperrings are studied and the relation between m-k-hyperideals and k-hyperideals on ordered semihyperrings are investigated.…”

“…In [22,23], the (m-)k-hyperideals of an ordered semihyperring are studied. In [23], the concept of derivation on ordered semihyperrings are studied and the relation between m-k-hyperideals and k-hyperideals on ordered semihyperrings are investigated. Omidi and Davvaz [24] tried to make connections between ordered semihyperrings by using 2-hyperideals.…”

“…In [25], the authors studied ordered semihyperrings to find a strongly regular relation such that the constructed quotient structure is an ordered semiring. Motivated by the above works on ordered semihyperrings [22][23][24][25], in this study, we define the concept of an (antitone) Galois connection between ordered semihyperrings; several properties are provided. Furthermore, we discuss the relationship between ordered semihyperrings by using two fundamental notions, the homomorphisms of ordered semihyperrings and the homo-derivations.…”