Results 11 to 20 of about 310 (116)
$r$-Hyperideals and Generalizations of $r$-Hyperideals in Krasner Hyperrings [PDF]
Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2021 This paper deals with Krasner hyperrings as an important class of algebraic hyperstructures. We investigate some properties of r-hyperideals in commutative Krasner hyperrings. Some properties of pr-hyperideals are also studied. The relation between prime hyperideals and r-hyperideals is investigated. We show that the image and the inverse image of an r-
Xu, Peng +5 more
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δ-r-hyperideals and φ-δ-r-hyperideals of commutative Krasner hyperrings [PDF]
Proceedings of the Estonian Academy of Sciences, 2023 In this paper, our purpose is to define the expansion of $r$-hyperideals and extend this concept to $ϕ$-$δ$-$r$-hyperideal. Let $\Re$ be a commutative Krasner hyperring with nonzero identity. Given an expansion $δ$ of hyperideals, a proper hyperideal $N$ of $\Re$ is called $δ$-$r$-hyperideal if $a\cdot b\in N$ with $ann(a)=0$ implies that $b\in δ(N ...
Xu, Peng +5 more
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A note on isomorphism theorems of Krasner (m, n)-hyperrings [PDF]
Arabian Journal of Mathematics, 2016 Recently, Krasner (m, n)-hyperrings were introduced and analyzed by Davvaz et. al. This is a suitable generalization of Krasner hyperrings. In this research work, we consider that if I is a normal hyperideal of a Krasner (m, n)-hyperring R, then the quotient hyperring [R : I*] is an (m, n)-ring.
Bijan Davvaz, S. Ostadhadi-Dehkordi
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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', +', ·').
K. Kwakpatoon +3 more
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Classes of F-hyperideals of a Krasner F^{(m,n)}-hyperring
Journal of Mahani Mathematical Research, 2022 Krasner F^{(m,n)}-hyperring were introduced and investigated by Farshi and Davvaz. In this paper, our purpose is to define and characterize three classes of F-hyperideals in a Krasner F^{(m,n)}-hyperring, namely, prime F-hyperideals, maximal F-hyperideals and primary F-hyperideals.
M. Anbarloei
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Exact category of hypermodules [PDF]
International Journal of Mathematics and Mathematical Sciences, Volume 2006, Issue 1, 2006., 2006 It is shown, among other things, that the category of hypermodules is an exact category, thus generalizing the classical ...
A. Madanshekaf
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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.
Burcu Nişancı Türkmen
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wsq-primary hyperideals of a Krasner (m,n)-hyperring
, 2023 In this paper we aim to introduce some hyperideals such as q-primary, (k,n)-absorbing q-primary, sq-primary, wsq-primary hyperideals.
M. Anbarloei
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Zariski topology of (Krasner) hyperrings [PDF]
22 ...
Ameri, Reza, Afshar, Behnam
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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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