Convex ordered Gamma-semihypergroups associated to strongly regular relations

Shao

et al. 2020

Front. Phys.

Self Cite

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.

Section: Preliminariesmentioning

confidence: 99%

“…We defineThen, S is a Γ-semihypergroup. We have (S, Γ, ≤ ) as an ordered Γ-semihypergroup[29], where the order relation ≤ is defined by≤ : {(a,a), (b, b), (c, c), (d, d), (e, e), (a, c), (b, a), (b, c), (d, a), (d, c), (e, a), (e, c)} . The covering relation and the figure of S are given by 3 {(a, c), (b, a), (d, a), (e, a)}.…”

mentioning

confidence: 99%

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

Shao

et al. 2020

Front. Phys.

Self Cite

“…Many researchers have studied (ordered) Γ-semihypergroups and their related notions, for instance, Omidi et al [8,9], Roa et al [10], and Tang et al [11], also see [12,13]. In [9], Omidi et al investigated the notion of (intra-) regular ordered Γ-semihypergroups associated with bi-Γ-hyperideals, and in [8], Omidi and Davvaz introduced the notion of convex ordered Γ-semihypergroups. In [14], Yaqoob and Tang investigated approximations of interior hyperfilters in partially ordered LA-semihypergroups.…”

Section: Introductionmentioning

confidence: 99%

“…) is an ordered 􏽑 i∈Ω Γ i -semihypergroup [8]. In the following, we study the behavior of weak (m, n)-Γ-hyperfilters on 􏽑 i∈Ω S i .…”

mentioning

confidence: 99%

Some Properties of Weak $Γ$ -Hyperfilters in Ordered $Γ$ -Semihypergroups

Mathematical Problems in Engineering

Chen

Kosari

et al. 2022

The main purpose of this paper is to study fundamental properties of weak Γ -hyperfilters on ordered Γ -semihypergroups that is a generalization of Γ -hyperfilters. Also, we investigate the relationship between weak Γ -hyperfilters and prime Γ -hyperideals in ordered Γ -semihypergroups. Finally, we introduce weak m , n - Γ -hyperfilters of ordered Γ -semihypergroups and conclude in paper with arising explicit theorems.

“…) is an ordered i∈Ω Γ i -semihypergroup [33]. In the following, we study the behavior of (m, n) − Γ-hyperfilters on the product of ordered Γ-semihypergroups.…”

mentioning

confidence: 99%

A Study on $A - I - Γ$ -Hyperideals and $(m, n) - Γ$ -Hyperfilters in Ordered $Γ$ -Semihypergroups

Discrete Dynamics in Nature and Society

Kosari

Shao

et al. 2021

Self Cite

The concept of almost interior Γ -hyperideals ( A − I − Γ -hyperideals) in ordered Γ -semihypergroups is a generalization of the concept of interior Γ -hyperideals ( I − Γ -hyperideals). In this study, the connections between I − Γ -hyperideals and A − I − Γ -hyperideals in ordered Γ -semihypergroups were presented. Also, we define the notion of m , n - Γ -hyperfilters of ordered Γ -semihypergroups and provide useful results on it. Moreover, we use the weak pseudoorders to construct quotient ordered Γ -semihypergroups by using ordered regular equivalence relations. These concepts lead us to a new research direction in ordered Γ -semihypergroups.