Prime and primary hyperideals in Krasner <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mrow><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>-hyperrings

Ameri, R.; Norouzi, Morteza

doi:10.1016/j.ejc.2012.08.002

Cited by 24 publications

(36 citation statements)

References 7 publications

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“…Since then, the theory of hyperstructures has been widely studied by many mathematicians. Let us mention at least some of them: Ameri and his school studied hypergroups, hypermodules, multialgebras, hyperideals, etc., in [4][5][6][7][8][9]. A recent paper of Asadi and Ameri deals with categorical connection between categories (m, n)-hyperrings and (m, n)-rings via the fundamental relation [10].…”

Section: Introductionmentioning

confidence: 99%

Superring of Polynomials over a Hyperring

2019

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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. One of the important subjects in the theory of hyperrings is the study of polynomials over a hyperring. Recently, polynomials over hyperrings have been studied by Davvaz and Musavi, and they proved that polynomials over a hyperring constitute an additive-multiplicative hyperring that is a hyperstructure in which both addition and multiplication are multivalued and multiplication is distributive with respect to the addition. In this paper, we first show that the polynomials over a hyperring is not an additive-multiplicative hyperring, since the multiplication is not distributive with respect to addition; then, we study hyperideals of polynomials, such as prime and maximal hyperideals and prove that every principal hyperideal generated by an irreducible polynomial is maximal and Hilbert’s basis theorem holds for polynomials over a hyperring.

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Section: Introductionmentioning

confidence: 99%

Superring of Polynomials over a Hyperring

2019

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“…Papers dealing with various aspects of n-ary hypergroups such as [2,13,17] usually need to work with the n-ary generalization of the concept of identity element and concepts similar to it. Let us include the respective definitions as well -yet when actually using them we expand them from hypergroups to semihypergroups. )…”

Section: Important Elementsmentioning

confidence: 99%

“…in [2]. The property of having a unique inverse element required in [2] is taken over from the definition of canonical n-ary hypergroup included in [15]. Notice that canonical n-ary hypergroups are a special class of commutative n-ary hyperstructures (moreover, with the unique identity e having a certain further property), i.e.…”

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confidence: 99%

“…Notice that canonical n-ary hypergroups are a special class of commutative n-ary hyperstructures (moreover, with the unique identity e having a certain further property), i.e. the definition of inverse elements included in [2], which has been taken over from [15], must be adjusted to a more general case.…”

mentioning

confidence: 99%

“…in [2]. The property of having a unique inverse element required in [2] is taken over from the definition of canonical n-ary hypergroup included in [15].…”

mentioning

confidence: 99%

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n–ary hyperstructures constructed from binary quasi–ordered semigroups

Novák

2014

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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Based on works by Davvaz, Vougiouklis and Leoreanu-Fotea in the field of n-ary hyperstructures and binary relations we present a construction of n-ary hyperstructures from binary quasi-ordered semigroups. We not only construct the hyperstructures but also study their important elements such as identities, scalar identities or zeros. We also relate the results to earlier results obtained for a similar binary construction and include an application of the results on a hyperstructure of linear differential operators.

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A study on a generalization of the n-ary prime hyperideals in a Krasner (m, n)-hyperring

Anbarloei

2021

Afr. Mat.

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Prime and primary hyperideals in Krasner (m,n)-hyperrings

Cited by 24 publications

References 7 publications

Superring of Polynomials over a Hyperring

Superring of Polynomials over a Hyperring

n–ary hyperstructures constructed from binary quasi–ordered semigroups

A study on a generalization of the n-ary prime hyperideals in a Krasner (m, n)-hyperring

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