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

Qiang, Xiaoli; Guan, Hao; Rashmanlou, Hossein

doi:10.3390/sym13122371

Cited by 7 publications

(5 citation statements)

References 9 publications

(9 reference statements)

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“…Weak pseudoorder on an ordered hyperstructure was investigated by Tang et al (2018), Rao, Kosari, et al (2021) and Qiang et al (2021). Clearly, ≤ is a weak pseudoorder, and also every pseudoorder relation is a weak pseudoorder.…”

Section: Weak Pseudoorder On Ordered Superringsmentioning

confidence: 99%

“…For the work done on ordered semihyperrings, we point out to Omidi and Davvaz (2018). Rao et al (2022) characterized ordered Γ-semihypergroups based on their weak Γ-hyperfilters. In addition, in Qiang et al (2021), w-pseudo-orders in ordered (semi)hyperrings are given.…”

mentioning

confidence: 99%

“…Rao et al (2022) characterized ordered Γ-semihypergroups based on their weak Γ-hyperfilters. In addition, in Qiang et al (2021), w-pseudo-orders in ordered (semi)hyperrings are given. Rao, Zhao, et al (2021); Rao, Kosari, et al (2021) introduced some new concepts of ordered hyperstructures.…”

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confidence: 99%

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A Survey on Weak Pseudoorders in Ordered Hyperstructures

Kosari¹,

Gheisari

Mirmohseni

et al. 2023

AIA

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As a generalization of pseudoorders, the weak pseudoorder in ordered (semi)hyperrings was defined by Qiang et al., and some results were studied. In order to further study, we apply weak pseudoorders for an ordered superring R and show relations with pseudoorders of R. Moreover, we present some illustrative examples and regular equivalence relation σ on ordered superring R, such that R/σ is an ordered superring. Furthermore, we show that if η is a weak pseudoorder on an ordered superring R, F is the set of all weak pseudoorders on R/η* and E ¼ fζ j ζ is a weak pseudoorder on R such that η ⊆ ζ}, then cardðEÞ ¼ cardðFÞ.

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Section: Weak Pseudoorder On Ordered Superringsmentioning

confidence: 99%

mentioning

confidence: 99%

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A Survey on Weak Pseudoorders in Ordered Hyperstructures

Kosari¹,

Gheisari

Mirmohseni

et al. 2023

AIA

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“…Recently, many authors, for example, those in Refs. [8,9], have investigated on ordered hyperstructures. Te paper given in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…In Ref. [9], w-pseudo-orders in ordered (semi)-hyperrings were defned, and some important properties are investigated.…”

Section: Introductionmentioning

confidence: 99%

Characterizations of Hyperideals and Interior Hyperideals in Ordered $Γ$ -Semihypergroups

Rao

Zhou

Cai

et al. 2022

Mathematical Problems in Engineering

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We give some conditions on ordered Γ -semihypergroups under which their interior hyperideal is equal to the hyperideal. In this paper, it is shown that in regular (resp., intraregular, semisimple) ordered Γ -semihypergroups, the hyperideals and the interior hyperideals coincide. To show the importance of these results, some examples and conclusions are provided.

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A Study on Special Kinds of Derivations in Ordered Hyperrings

et al. 2022

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In this study, we concentrate on an important class of ordered hyperstructures with symmetrical hyperoperations, which are called ordered Krasner hyperrings, and discuss strong derivations and homo-derivations. Additionally, we apply our results on nonzero proper hyperideals to the study of derivations of prime ordered hyperrings. This work is a pioneer in studies on structures such as hyperideals and homomorphisms of an ordered hyperring with the help of derivation notation. Finally, we prove some results on 2-torsion-free prime ordered hyperrings by using derivations. We show that if d is a derivation of 2-torsion-free prime hyperring R and the commutator set [l,d(q)] is equal to zero for all q in R, then l∈Z(R). Moreover, we prove that if the commutator set (d(l),q) is equal to zero for all l in R, then (d(R),q)=0.

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

Abstract: In this work, we study the notion of w-pseudo-order on an ordered (semi)hyperring and give some explicit examples. In addition, we give some examples to compare weak pseudo-order relations with pseudo-order relations. Finally, we construct ordered (semi)hyperrings using regular relations.

Cited by 7 publications

References 9 publications

A Survey on Weak Pseudoorders in Ordered Hyperstructures

A Survey on Weak Pseudoorders in Ordered Hyperstructures

Characterizations of Hyperideals and Interior Hyperideals in Ordered $Γ$ -Semihypergroups

A Study on Special Kinds of Derivations in Ordered Hyperrings

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

Abstract: In this work, we study the notion of w-pseudo-order on an ordered (semi)hyperring and give some explicit examples. In addition, we give some examples to compare weak pseudo-order relations with pseudo-order relations. Finally, we construct ordered (semi)hyperrings using regular relations.

Cited by 7 publications

References 9 publications

A Survey on Weak Pseudoorders in Ordered Hyperstructures

A Survey on Weak Pseudoorders in Ordered Hyperstructures

Characterizations of Hyperideals and Interior Hyperideals in Ordered Γ -Semihypergroups

A Study on Special Kinds of Derivations in Ordered Hyperrings

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Product

Resources

About

Characterizations of Hyperideals and Interior Hyperideals in Ordered $Γ$ -Semihypergroups