Normal hyperideals in Krasner (<i>m, n</i>)-hyperrings

Norouzi, Morteza; Ameri, R.; Leoreanu-Fotea, V.

doi:10.2478/auom-2018-0041

Cited by 10 publications

(11 citation statements)

References 18 publications

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“…al. proposed and analysed a new defnition for normal hyperideals in Krasner (m, n)-hyperrings, with respect to that one given in [25] and they showed that these hyperideals correspond to strongly regular relations [27]. Asadi and Ameri introduced and studied direct limit of a direct system in the category of Krasner (m, n)-hyperrigs [6].…”

Section: Introductionmentioning

confidence: 99%

Extensions of $n$-ary prime hyperideals via an $n$-ary multiplicative subset in a Krasner $(m,n)$-hyperring

Anbarloei¹

2022

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Let R be a Krasner (m, n)-hyperring and S be an n-ary multiplicative subset of R. The purpose of this paper is to introduce the notion of n-ary S-prime hyperideals as a new expansion of n-ary prime hyperideals. A hyperideal I of R disjoint with S is said to be an n-ary S-prime hyperideal if there exists s ∈ S such that whenever g(x n 1 ) ∈ I for all x n 1 ∈ R, then g(s, x i , 1 (n−2) ) ∈ I for some 1 ≤ i ≤ n. Several properties and characterizations concerning n-ary S-prime hyperideals are presented. The stability of this new concept with respect to various hyperring-theoretic constructions are studied. Furthermore, we extend this concept to n-ary S-primary hyperideals. We obtained some specific results explaining the structure.2010 Mathematics Subject Classification. 16Y99. Key words and phrases.n-ary J-hyperideal, n-ary δ-J-hyperideal, (k, n)-absorbing δ-Jhyperideal.

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Section: Introductionmentioning

confidence: 99%

Extensions of $n$-ary prime hyperideals via an $n$-ary multiplicative subset in a Krasner $(m,n)$-hyperring

Anbarloei¹

2022

Preprint

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“…Ameri and Norouzi in [1] introduced some important hyperideals such as Jacobson radical, n-ary prime and primary hyperideals, nilradical, and n-ary multiplicative subsets of Krasner (m, n)-hyperrings. For more study on Krasner (m, n)-hyperring refer to [2,3,4,15,24,26,28,31].…”

Section: Introductionmentioning

confidence: 99%

Classes of F-hyperideals of a Krasner F^{(m,n)}-hyperring

Anbarloei¹

2022

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Krasner F (m,n) -hyperrings were introduced and investigated by Farshi and Davvaz. In this paper, our purpose is to define and characterize three particular classes of F -hyperideals in a Krasner F (m,n) -hyperring, namely prime F -hyperideals, maximal F -hyperideals and primary F -hyperideals, which extend similar concepts of ring context. Furthermore, we examine the relations between these structures. Then a number of major conclusions are given to explain the general framework of these structures.Key words and phrases. prime F -hyperideal, maximal F -hyperideal, primary F -hyperideal, Krasner F (m,n) -hyperring. * ) be the set of all fuzzy subsets of G.the following conditions are satisfied: (1) (a•b)•c = a•(b•c) for all a, b, c ∈ G, (2) there exists e ∈ G with a ∈ supp(a•e∩e•a), for all a ∈ G, (3) for each a ∈ G, there exists a unique element afor all a, b, c ∈ G. Indeed, a fuzzy hyperoperation assigns to each pair of elements of G a non-zero fuzzy subset of G, while a hyperoperation assigns to each pair of elements of G a non-empty subset of G. The concepts of Krasner F (m,n) -hyperrings and F -hyperideals were defined in [14] by Farshi and Davvaz. In this paper, we continue the study of F -hyperideals of a Krasner F (m,n) -hyperring, initiated in [14]. We define and analyze there particular types of F -hyperideals in a Krasner F (m,n) -hyperring, maximal F -hyperideals and primary F -hyperideals. We investigate the connections between them. Moreover, we introduce the concepts of F -radical, quotient Krasner F (m,n) -hyperring and Jacobson radical. The overall framework of these structures is then explained. It is shown (Theorem 4.6) that if Q is an primary F -hyperideal of a Krasner F (m,n)hyperring (R, f, g), then √ Q F is a prime F -hyperideal of R. PreliminariesIn this section we recall some basic terms and definitions from [14] which we need to develop our paper.

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“…Hence, new ways to reduce emissions of carbon dioxide are under development. [1][2][3] In addition, because of useful and practical aspects of gas hydrate phenomenon, the necessary of further researches in * Corresponding author: a.bozorgian@mhrian.ac.ir this field is clarified. Since a few decades ago, the presence of large amounts of natural gas has been proven which stored in gaseous hydrates in the ocean's bed and the poles.…”

Section: Introduction *mentioning

confidence: 99%

“…The hydrate structure resulting from the interaction of physical forces among the stocked gas molecules and stable water molecules. 2,5,[7][8][9][10][11] In recent decades, several studies have been carried out on the kinetics of the formation and degradation of gas hydrates, due to the ability of gas hydrates to transport gas, and also existence of massive hydrocarbon resources as hydrates in the nature. In this study, laboratory data for the kinetics of the CO 2 hydrates formation in the presence of a promoter and surfactants were obtained within a certain range of temperature and pressure, in a fixed volume reactor.…”

Section: Introduction *mentioning

confidence: 99%

Determination of CO2 gas hydrates surface tension in the presence of nonionic surfactants and TBAC

Bozorgian¹,

Aboosadi²,

Mohammadi³

et al. 2021

Rev.Roum.Chim.

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The gas hydrates formation, in spite of its disadvantages, has some advantages such as separating, transferring and storing gas. Therefore, determining the appropriate promoters for the gas hydrates’ formation is as important as selecting an appropriate inhibitor. One of the effective promoters is tetra-n-butyl ammonium chloride (TBAC). Due to TBAC non-destructive environmental effects and its extraordinary effect on the thermodynamics of gas hydrates, this salt is one of the most widely used promoters. TBAC was discussed in the context of hydrate structure formation and Alkyl Poly Glucoside (APG) as a nonionic surfactant, because of its characteristics like biodegradability, emulsifiers and reasonable prices. In this study, the surface tension between Co2 hydrates was determined at constant temperatures and pressures with different concentrations. For this purpose, the classical nucleation theory has been used. The experimental data show that at constant temperature, the induction time is reduced by increasing TBAC concentration and adding APG. Also, the surface tension value reduces significantly due to adding APG, which this reduction has led to an upward trend with increasing temperature. Finally, the surface tension values obtained from the developed method were compared by presented correlations.

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Normal hyperideals in Krasner (m, n)-hyperrings

Cited by 10 publications

References 18 publications

Extensions of $n$-ary prime hyperideals via an $n$-ary multiplicative subset in a Krasner $(m,n)$-hyperring

Extensions of $n$-ary prime hyperideals via an $n$-ary multiplicative subset in a Krasner $(m,n)$-hyperring

Classes of F-hyperideals of a Krasner F^{(m,n)}-hyperring

Determination of CO2 gas hydrates surface tension in the presence of nonionic surfactants and TBAC

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