On α-Relation and Transitivity Conditions of α

Mirvakili, S.; Anvariyeh, S. M.; Davvaz, B.

doi:10.1080/00927870801937364

Cited by 25 publications

(6 citation statements)

References 11 publications

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“…Then, this relation is investigated in [59]. Also, a similar relation is defined on hypermodules to obtain an ordinary module [13,14,58]. The largest class of hyperstructures called H v -structures.…”

Section: Fundamental Relations On Hyperstructuresmentioning

confidence: 99%

A brief survey on algebraic hyperstructures: Theory and applications

Davvaz

2020

JAHLA

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I am working on algebraic hyperstructures from 1995. During the last twenty years, I together with my students and co-authors studied and developed the theory of algebraic hyperstructures in many directions. In particular, we tried to find real examples of hyperstructures in nature. In this paper we review some parts of these works such as (1) Fundamental relations on hyperstructures; (2) Fuzzy sets and hyperstructures; (3) Rough sets and hyperstructures; (4) Topology and hyperstructures; (5) Number theory and hyperstructures; (6) n-ary hypergroups and there extension to hyperrings and hypermodules; (7) Applications of hyperstructures in biology, physics and chemistry.

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Section: Fundamental Relations On Hyperstructuresmentioning

confidence: 99%

A brief survey on algebraic hyperstructures: Theory and applications

Davvaz

2020

JAHLA

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“…. If α * is the transitive closure of α, then α * is a strongly regular relation both on (R, +) and (R, •), and the quotient R/α * is a commutative ring [9], also see [13].…”

Section: Definition 2 [9]mentioning

confidence: 99%

Construction of (M, N)-hypermodule over (R, S)-hyperring

Mirvakili

Anvariyeh

Davvaz

2019

Acta Universitatis Sapientiae, Mathematica

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“…Davvaz and Leoreanu-Fotea [5] published a book titled Hyperring Theory and Applications. The hyperrings were studied by many authors, for example see [4,7,11,12,13,15]. In [1], Babaeia et al introduced the notion of ℜ-parts in hyperrings as a generalization of complete parts in hyperrings.…”

Section: Introductionmentioning

confidence: 99%

Finitely generated rings obtained from hyperrings through the fundamental relations

2021

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In this article, we introduce and analyze a strongly regular relation $\omega^{*}_{\mathcal{A}}$ on a hyperring$R$ such that in a particular case we have $|R/\omega^{*}_{\mathcal{A}}|\leq 2$ or$R/\omega^{*}_{\mathcal{A}}=<\omega^{*}_{\mathcal{A}}(a)>$, i.e., $R/\omega^{*}_{\mathcal{A}}$ is a finite generated ring. Then, by using the notion of $\omega^{*}_{\mathcal{A}}$-parts, we investigate the transitivity condition of $\omega_{\mathcal{A}}$. Finally, we investigate a strongly regular relation $\chi^{*}_{\mathcal{A}}$ on the hyperring $R$ such that $R/\chi^{*}_{\mathcal{A}}$ is a commutative ring with finite generated.

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On α-Relation and Transitivity Conditions of α

Cited by 25 publications

References 11 publications

A brief survey on algebraic hyperstructures: Theory and applications

A brief survey on algebraic hyperstructures: Theory and applications

Construction of (M, N)-hypermodule over (R, S)-hyperring

Finitely generated rings obtained from hyperrings through the fundamental relations

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