Results 31 to 40 of about 117 (89)
Height of prime hyperideals in Krasner hyperrings
Filomat, 2017 Extending the notion of dimension of a hyperring, we introduce the concept of height of a prime hyperideal of a hyperring, similarly as in ring theory, and we present some basic properties and relations with the dimension notion. In the second part of the article we illustrate some results concerning the height of prime hyperideals in ...
Cristea, Irina Elena, Bordbar, Hashem
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On Prime Hyperideals of a Krasner Hyperring
Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2022 The basis of this study, which was put forth in order to appropriate a special area in the hyperring theory, which has recently been studied as a generalization of the ring theory, which uses the module theory as an application field, is based on integrally closed Krasner hyperrings and (almost) integral dependence applications in krasner hyperrings.
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Hopkins-Levitzki theorem for Krasner hyperrings
Filomat, 2021 In this paper, our aim is to generalize and extend the Hopkins-Levitzki theorem from noncommutative rings to Krasner hyperring. Also, we prove that a Krasner hyperring R is Noetherian if and only if it satisfies the ascending chain conditions of prime hyperideals.
S. Ostadhadi-Dehkordi, K.P. Shum
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On Fuzzy Ordered Hyperideals in Ordered Semihyperrings
Advances in Fuzzy Systems, Volume 2019, Issue 1, 2019., 2019 In this paper, we introduce the concept of fuzzy ordered hyperideals of ordered semihyperrings, which is a generalization of the concept of fuzzy hyperideals of semihyperrings to ordered semihyperring theory, and we investigate its related properties. We show that every fuzzy ordered quasi‐hyperideal is a fuzzy ordered bi‐hyperideal, and, in a regular ...
O. Kazancı +3 more
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δ‐Primary Hyperideals on Commutative Hyperrings
International Journal of Mathematics and Mathematical Sciences, Volume 2017, Issue 1, 2017., 2017 The purpose of this paper is to define the hyperideal expansion. Hyperideal expansion is associated with prime hyperideals and primary hyperideals. Then, we define some of their properties. Prime and primary hyperideals’ numerous results can be extended into expansions.
Elif Ozel Ay +3 more
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States and Measures on Hyper BCK‐Algebras
Journal of Applied Mathematics, Volume 2014, Issue 1, 2014., 2014 We define the notions of Bosbach states and inf‐Bosbach states on a bounded hyper BCK‐algebra (H, ∘, 0, e) and derive some basic properties of them. We construct a quotient hyper BCK‐algebra via a regular congruence relation. We also define a ∘‐compatibled regular congruence relation θ and a θ‐compatibled inf‐Bosbach state s on (H, ∘, 0,e). By inducing
Xiao-Long Xin, Pu Wang, Baolin Wang
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On σ-derivations of Krasner hyperrings
Gulf Journal of MathematicsWe present a significant extension of the derivation concept to Krasner hyperrings, namely the σ-derivation, which is defined utilizing a self-mapping σ on the hyperring R. We investigate several important properties of these σ-derivations and explore their behavior in prime Krasner hyperrings. Furthermore, we establish conditions under which a Krasner
Leerawat, Utsanee +2 more
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Associate, Hyperdomainlike, and Presimplifiable Hyperrings
Journal of Mathematics, Volume 2014, Issue 1, 2014., 2014 Based on the works of Axtell et al., Anderson et al., and Ghanem on associate, domainlike, and presimplifiable rings, we introduce new hyperrings called associate, hyperdomainlike, and presimplifiable hyperrings. Some elementary properties of these new hyperrings and their relationships are presented.
Agboola Adesina Abdul Akeem +2 more
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Classical prime subhypermodules and related extensions [PDF]
Categories and General Algebraic Structures with ApplicationsIn this paper, we extend the notion of prime subhypermodulesto $n$-ary classical prime, $n$-ary weakly classical prime and $n$-ary $\phi$-classical prime subhypermodules of an $(m,n)$-hypermodule over a commutative Krasner $(m,n)$-hyperring.
Mahdi Anbarloei
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Note on Isomorphism Theorems of Hyperrings
International Journal of Mathematics and Mathematical Sciences, Volume 2010, Issue 1, 2010., 2010 There are different notions of hyperrings (R, +, ·). In this paper, we extend the isomorphism theorems to hyperrings, where the additions and the multiplications are hyperoperations.
Muthusamy Velrajan +2 more
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