Localization of Hoop - Algebras

Ghorbani, Shokoofeh

doi:10.5373/jarpm.1378.032812

Cited by 6 publications

(4 citation statements)

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“…Recent investigations are concerned with non-commutative generalizations for these structures. During these years, many researchers study on hoops in different way, and got some results on hoops [11,20,23,26]. Algebra and topology, the two fundamental domains of mathematics, play complementary roles.…”

Section: Introductionmentioning

confidence: 99%

Quotient Hoops Induced by Quasi-Valuation Maps

BORZOOEI¹,

REZAEI²,

KOLOGANI³

et al. 2022

KgJMat

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In this paper, our aim was making a metric space on hoop algebras, because of that, we introduced the notion of valuation maps from F-quasi-valuation map based on hoops and related properties of them are investigated. By using these notions, we introduced a quasi-metric space. The continuity of operations of a hoop is studied with topology induced by a quasi-valuation. Also, we studied hoop homomorphism and investigated that under which condition this homomorphism is an F-quasi-valuation map. Moreover, we wanted to ﬁnd a congruence relation on hoops in a new way and study about the quotient structure that is made by it. So, we deﬁned a congruence relation by F-quasi-valuation map and proved that the quotient is a hoop.

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Section: Introductionmentioning

confidence: 99%

Quotient Hoops Induced by Quasi-Valuation Maps

BORZOOEI¹,

REZAEI²,

KOLOGANI³

et al. 2022

KgJMat

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“…The hoop, which was introduced by Bosbach in [1,2], is naturally-ordered commutative residuated integral monoids. Several properties of hoops are displayed in [3][4][5][6][7][8][9][10][11][12][13][14]. The idea of the quasi-coincidence of a fuzzy point with a fuzzy set, which was introduced in [15], has played a very important role in generating fuzzy subalgebras of BCK/BCI-algebras, called (α, β)-fuzzy subalgebras of BCK/BCI-algebras, introduced by Jun [16].…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Filters of Hoops Based on Fuzzy Points

Kologani¹,

Takallo

Kim

2019

Mathematics

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“…After that in [6], they studied these notions in pseudo-hoops. Moreover, in [7,8], researchers investigated n-fold filters, nodal filters and etc, on hoops. Several properties of hoops are displayed in [3][4][5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, in [7,8], researchers investigated n-fold filters, nodal filters and etc, on hoops. Several properties of hoops are displayed in [3][4][5][6][7][8][9][10][11]. The idea of quasi-coincidence of a fuzzy point with a fuzzy set is mentioned in [12], and it played a vital role to generate some different types of fuzzy subalgebras in of BCK/BCI-algebras, called on (α, β)-fuzzy subalgerbas of BCK/BCI-algebras which is introduced by Jun [13].…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Positive Implicative Filters of Hoops Based on Fuzzy Points

Borzooei

Kologani²,

Kish

et al. 2019

Mathematics

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In this paper, we introduce the notions of ( ∈ , ∈ ) -fuzzy positive implicative filters and ( ∈ , ∈ ∨ q ) -fuzzy positive implicative filters in hoops and investigate their properties. We also define some equivalent definitions of them, and then we use the congruence relation on hoop defined in blue[Aaly Kologani, M.; Mohseni Takallo, M.; Kim, H.S. Fuzzy filters of hoops based on fuzzy points. Mathematics. 2019, 7, 430; doi:10.3390/math7050430] by using an ( ∈ , ∈ ) -fuzzy filter in hoop. We show that the quotient structure of this relation is a Brouwerian semilattice.

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Localization of Hoop - Algebras

Cited by 6 publications

References 0 publications

Quotient Hoops Induced by Quasi-Valuation Maps

Quotient Hoops Induced by Quasi-Valuation Maps

Fuzzy Filters of Hoops Based on Fuzzy Points

Fuzzy Positive Implicative Filters of Hoops Based on Fuzzy Points

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