Results 31 to 40 of about 255 (98)
On Homomorphisms of Krasner Hyperrings
Annals of the Alexandru Ioan Cuza University - Mathematics, 2011 On Homomorphisms of Krasner Hyperrings By a homomorphism from a Krasner hyperring (A, +, ·) into a Krasner hyperring (A', +', ·') we mean a function ƒ: A → A' satisfying ƒ(x + y) ⊆ ƒ(x)+ ƒ(y) and ƒ(x · y) = ƒ(x) ·' ƒ(y) for all ×, y ∈ A. The kernel of ƒ, ker ƒ, is defined by ker ƒ = {x ∈ A | ƒ(x) = 0'} where 0' is the zero of (A', +', ·').
Phanthawimol, W. +3 more
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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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Superring of Polynomials over a Hyperring
Mathematics, 2019 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.
Reza Ameri +2 more
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On d-prime hyperideals of hyperrings [PDF]
Journal of HyperstructuresFor Krasner hyperrings, we study d-prime hyperideals where d is a homo-derivation. Furthermore, we show that every maximal d-hyperideal and d-prime hyperideal is a prime hyperideal of a commutative hyperring.
Maryam Akhoundi, Saber Omidi
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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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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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Relations on Krasner \((m,n)\)-hyperrings.
European Journal of Combinatorics, 2010 \textit{G. Crombez} [Abh. Math. Semin. Univ. Hamb. 37, 180-199 (1972; Zbl 0247.08001)] generalized the concept of rings to the case of \(n\)-ary operations. Now this concept is extended to \(n\)-ary hyperoperations. Very elementary properties of such hyper-algebras are proved.
Mirvakili, S., Davvaz, B.
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