Commutative Rings Obtained from Hyperrings (Hv-rings) with α∗-Relations

Davvaz, Bijan; Vougiouklis, Thomas

doi:10.1080/00927870701410629

Cited by 57 publications

(51 citation statements)

References 9 publications

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“…A comprehensive review of hyperrings theory is covered in Davvaz and Vougiouklis [9], Spartalis [24], Vougiouklis [30] and in the book [8] written by Davvaz and Leoreanu-Fotea. In the following, we consider one of the most general types of hyperrings.…”

Section: Basic Definitions and Preliminariesmentioning

confidence: 99%

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Foundations of Ordered (Semi)hyperrings

Davvaz

Omidi

2017

JIMS

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Abstract. In the present paper, we introduce the notion of (semi)hyperring (R, +, ·) together with a suitable partial order ≤. This structure is called an ordered (semi)hyperring. Also, we present several examples of ordered (semi)hyperrings and prove some results in this respect. By using the notion of pseudo order on an ordered (semi)hyperring (R, +, ·, ≤), we obtain an ordered (semi)ring. Finally, we study some properties of pseudoorder on an ordered (semi)hyperring.Key words and Phrases: Algebraic hyperstructure, ordered (semi)hyperring, strongly regular relation, pseudoorder. Abstrak. Dalam makalah ini diperkenalkan notasi dari (semi)hyperring (R, +, ·)bersama dengan suatu suitable partial order ≤. Struktur ini disebut ordered (semi)hyperring. Beberapa contoh dari ordered (semi)hyperring disajikan dan dibuktikan. Dengan menggunakan notasi dari pseudoorder pad suatu ordered (semi)hyperring (R, +, ·, ≤), diperoleh suatu ordered (semi)ring. Beberapa sifat dari pseudoorder pad suatu ordered (semi)hyperring.Kata kunci: Algebraic hyperstructure, ordered (semi)hyperring, strongly regular relation, pseudoorder.

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Section: Basic Definitions and Preliminariesmentioning

confidence: 99%

“…The more general structure that satisfies the ring-like axioms is the hyperring in the general sense. De Salvo [11] studied hyperrings in which the additions and the multiplications were hyperoperations; also see [1,9,23,27,30]. We refer the reader to Davvaz and Leoreanu-Fotea [8] for basic notions updated to 2007 of hyperring theory.…”

Section: Introductionmentioning

confidence: 99%

Foundations of Ordered (Semi)hyperrings

Davvaz

Omidi

2017

JIMS

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“…Rota [15] introduced a multiplicative hyperring, where + is a binary operation and the multiplication is a hyperoperation. De Salvo [8] studied hyperrings in which the additions and the multiplications were hyperoperations, also see [7,16]. In 2007, Davvaz and Leoreanu-Fotea [5] published a book titled Hyperring Theory and Applications.…”

Section: Introductionmentioning

confidence: 99%

A class of hyperrings connected to preordered generalized Γ-rings

Jafarpour

Aghabozorgi

Davvaz

2015

European Journal of Combinatorics

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a r t i c l e i n f o Article history: Available online xxxx a b s t r a c tIn this paper, we define the notion of preordered weak Γ -rings as a generalization of the concept of Γ -rings, the basic properties of prime ideals in weak Γ -rings are developed. At the end we construct a class of hyperrings in the sense of Rota from weak Γ -rings and also a connection between morphisms of the weak Γ -rings and the morphism of associated weak Γ -hyperrings has been investigated.

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“…Basic definitions and propositions about the hyperstructures are found in [1,2,5,19]. Krasner [13] has studied the notion of hyperfields, hyperrings, and then some researchers, namely, Davvaz [3,7,10], Vougiouklis [19,20] and others followed him.…”

Section: Introductionmentioning

confidence: 99%

An introduction to the theory of algebraic multi-hyperring spaces

Hila¹,

Davvaz²

2014

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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A Smarandache multi-space is a union of n different spaces equipped with some different structures for an integer n ≥ 2 which can be used both for discrete or connected spaces, particularly for geometries and spacetimes in theoretical physics. In this paper, applying the Smarandaches notion and combining this with hyperrings in hyperring theory, we introduce the notion of multi-hyperring space and initiate a study of multi-hyperring theory. Some characterizations and properties of multihyperring spaces are investigated and obtained. Some open problems are suggested for further study and investigation.

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Commutative Rings Obtained from Hyperrings (H_v-rings) with α∗-Relations

Cited by 57 publications

References 9 publications

Foundations of Ordered (Semi)hyperrings

Foundations of Ordered (Semi)hyperrings

A class of hyperrings connected to preordered generalized Γ-rings

An introduction to the theory of algebraic multi-hyperring spaces

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