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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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weakly $ (k,n) $-absorbing (primary) hyperideals of a Krasner $ (m,n) $-hyperring
Hacettepe Journal of Mathematics and Statistics, 2023 In this paper, we introduce new expansion classes, namely weakly $ (k,n) $-absorbing hyperideals and weakly $ (k,n) $-absorbing primary hyperideals of a Krasner $ (m,n) $-hyperring, including $ (k,n) $-absorbing hyperideal and $ (k,n) $-absorbing primary
B. Davvaz, G. Ulucak, Ünsal Teki̇r
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Krasner (m,n)-hyperring of fractions [PDF]
, 2022 The formation of rings of fractions and the associated process of localization are the most important technical tools in commutative algebra. Krasner (m,n)-hyperrings are a generalization of (m,n)-ring. Let R be a commutative Krasner (m,n)-hyperring.
M. Anbarloei
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$J$-hyperideals and their expansions in a Krasner $(m,n)$-hyperring
Hacettepe Journal of Mathematics and Statistics, 2022 Over the years, different types of hyperideals have been introduced in order to let us fully realize the structures of hyperrings in general. The aim of this research work is to define and characterize a new class of hyperideals in a Krasner $(m,n)
M. Anbarloei
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On hyperideals of Krasner hyperrings based on derived unitary rings [PDF]
Journal of Mahani Mathematical Research, 2022 In this paper first, we introduce and analyze the strongly regular relations $\lambda^*_{e}$ and $\Lambda^*_{e}$ on a hyperring such that the derived quotient ring is unitary and unitary commutative, respectively. Next, we define and study the notion of $
Seyed Shahin Mousavi +3 more
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δ-primary subhypermodules on Krasner hyperrings [PDF]
Categories and General Algebraic Structures with ApplicationsIn this paper, we study commutative Krasner hyperrings with nonzero identity and nonzero unital hypermodules. We introduce a new concept, the $\delta$-primary subhypermodule on Krasner hyperrings.
Kostaq Hila +5 more
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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', +', ·').
Witthawas Phanthawimol +3 more
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$r$-Hyperideals and Generalizations of $r$-Hyperideals in Krasner Hyperrings [PDF]
, 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-
Peng Xu +5 more
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Various Kinds of Freeness in the Categories of Krasner Hypermodules
International Journal of Analysis and Applications, 2018 The purpose of this paper is to study the concept of freeness in the categories of Krasner hypermodules over a Krasner hyperring. In this regards first we construct various kinds of categories of hypermodules based on various kinds of homomorphisms of ...
Hossein Shojaei, Reza Ameri
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Operations on hyperideals in ordered Krasner hyperrings [PDF]
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016 In the present paper, we will concentrate our efforts on ordered Krasner hyperrings and investigate some of their related properties. Moreover, we introduce and analyze the notion of interior hyperideal in ordered Krasner hyperrings. We also characterize
Omidi S., Davvaz B., Corsini P.
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