A further study on ordered regular equivalence relations in ordered semihypergroups

Tang, Jian; Feng, Xinyang; Davvaz, Bijan; Xie, Xiang-Yun

doi:10.1515/math-2018-0016

Cited by 18 publications

(17 citation statements)

References 16 publications

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“…Throughout this paper, we shall use the notions and notations of [1,4,8,14]. [1]) Let N be the set of all non-negative integers and put I = N × N, S = N ∪ I.…”

Section: Preliminariesmentioning

confidence: 99%

A characterization of translational hulls of a strongly right type B semigroup

2019

Open Mathematics

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The aim of this paper is to study the translational hull of a strongly right type B semigroup. Our main result is to prove that the translational hull of a strongly right type B semigroup is itself a strongly right type B semigroup. As an application, we give a proof of a problem posted by Petrich on translational hulls of inverse semigroups in Petrich (Inverse Semigroups, Wiley, New York, 1984) to the cases of some strongly right type B semigroups.

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“…Throughout this paper, we shall use the notions and notations of [1,4,8,14]. [1]) Let N be the set of all non-negative integers and put I = N × N, S = N ∪ I.…”

Section: Preliminariesmentioning

confidence: 99%

A characterization of translational hulls of a strongly right type B semigroup

2019

Open Mathematics

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“…In 2016, Gu and Tang [15] studied an open problem for ordered semihypergroups and established a partial solution. Next, Tang et al [16] studied the further properties of ordered regular equivalence relations in ordered semihypergroups. Moreover, the authors gave a complete answer of the open problem given by Davvaz et al in [14].…”

Section: Introductionmentioning

confidence: 99%

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

Rao

Kosari

Shao

et al. 2021

Discrete Dynamics in Nature and Society

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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.

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“…Ordered semihypergroups are suggested by Heidari and Davvaz [4] and then investigated by Davvaz et al in [5] (also, see [6][7][8]).…”

Section: Introductionmentioning

confidence: 99%

“…e research about generalization of hyperideals in ordered hyperstructures is growing rapidly [9,10]. In recent years, pseudoorders have received extensive attention in ordered hyperstructures [5,8]. Using the notion of (weak) pseudoorder [5,8], several examples of ordered semi (hyper) groups have been constructed in connection with ordered semihypergroups.…”

Section: Introductionmentioning

confidence: 99%

“…In recent years, pseudoorders have received extensive attention in ordered hyperstructures [5,8]. Using the notion of (weak) pseudoorder [5,8], several examples of ordered semi (hyper) groups have been constructed in connection with ordered semihypergroups. Weak pseudoorders can remarkably support the constructions of ordered semihypergroups [8].…”

Section: Introductionmentioning

confidence: 99%

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