Topological hypergroupoids

Hošková-Mayerová, Šárka

doi:10.1016/j.camwa.2012.04.017

Cited by 41 publications

(15 citation statements)

References 7 publications

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“…The following lemma give us a topology on P * (H ) induced by τ . Lemma 2.1 [16] Let (H, τ ) be a topological space. Then, the family B consisting of all sets S V = {U ∈ P * (H ) | U ⊆ V, U ∈ τ } is a base for a topology on P * (H ).…”

Section: Topological Algebraic Hyperstructuresmentioning

confidence: 99%

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Topological Polygroups

Heidari

Davvaz

Modarres

2015

Bull. Malays. Math. Sci. Soc.

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This paper deals with certain algebraic systems called polygroups. A polygroup is a completely regular, reversible in itself hypergroup. The concept of topological polygroups is a generalization of the concept of topological groups. In this paper, we present the concept of topological hypergroups and prove some properties. Then, we define the notion of topological polygroups. By considering the relative topology on subpolygroups we prove some properties of them. Finally, the topological isomorphism theorems of topological polygroups are proved.

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Section: Topological Algebraic Hyperstructuresmentioning

confidence: 99%

“…Then, this concept was studied by many authors, for example, see [5,6,10,11,17,22,23]. Till now, only a few papers treated the notion of topological hyperstructures, in the classical and fuzzy case, see [2,7,8,14,16]. Let (H 1 • an isomorphism if it is a homomorphism, and its inverse f −1 is a homomorphism, too.…”

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confidence: 97%

Topological Polygroups

Heidari

Davvaz

Modarres

2015

Bull. Malays. Math. Sci. Soc.

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“…Then, Γ * is the smallest equivalence relation on R, such that the quotient space R/Γ * is a ring, and it is called the fundamental relation of R and R/Γ * is called fundamental ring of R (for more details, see [12]). Definition 3.…”

Section: Preliminariesmentioning

confidence: 99%

“…Th. Vougiouklis studied the fundamental relation in hyperrings and the general hyperfield in his paper [12]. Extension of elliptic curves on Krasner hyperfields was studied in [13].…”

Section: Introductionmentioning

confidence: 99%

Superring of Polynomials over a Hyperring

2019

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A Krasner hyperring (for short, a hyperring) is a generalization of a ring such that the addition is multivalued and the multiplication is as usual single valued and satisfies the usual ring properties. One of the important subjects in the theory of hyperrings is the study of polynomials over a hyperring. Recently, polynomials over hyperrings have been studied by Davvaz and Musavi, and they proved that polynomials over a hyperring constitute an additive-multiplicative hyperring that is a hyperstructure in which both addition and multiplication are multivalued and multiplication is distributive with respect to the addition. In this paper, we first show that the polynomials over a hyperring is not an additive-multiplicative hyperring, since the multiplication is not distributive with respect to addition; then, we study hyperideals of polynomials, such as prime and maximal hyperideals and prove that every principal hyperideal generated by an irreducible polynomial is maximal and Hilbert’s basis theorem holds for polynomials over a hyperring.

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“…The most well-known constructions of hypergroupoids from binary relations are those proposed by Rosenberg [22], Corsini-Leoreanu [8,9], Spartalis [24,25], Cristea-Ştefȃnescu [10,11,12], extended later to n-ary hypergroupoids by Davvaz, Leoreanu-Fotea [13], or to actions of hyperstructures by Chvalina et al [6], or to topological hypergroups by Hoskova [17] . Feng [15] obtained fuzzy hypergroups from fuzzy relations, while Jančić-Rašović in [21] constructed hyperrings from fuzzy relations defined on a semigroup.…”

Section: Introductionmentioning

confidence: 99%