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Keywords: hyperoperation, hypergroupoid, dependence relation, influence, impact
Published in RUNG: 24.09.2019; Views: 3765; Downloads: 145
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Keywords: cyclic group, cyclic hypergroup, EL-hyperstructure, preorder
Published in RUNG: 08.11.2018; Views: 4040; Downloads: 0
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Keywords: composition hyperring, partially ordered semigroup, hyperstructure
Published in RUNG: 30.10.2017; Views: 4518; Downloads: 0
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Abstract: Inspired by the classical concept of height of a prime ideal in a ring, we proposed in a precedent paper the notion of height of a prime hyperideal in a Krasner hyperring. In this note we first generalize some results concerning the height of a prime hyperideal in a Noetherian Krasner hyperring, with the intent to extend this definition to the case of a general hyperideal in a such hyperring. The main results in this note show that, in a commutative Noetherian Krasner hyperring, the height of a minimal prime hyperideal over a proper hyperideal generated by n elements is less than or equal to n, the converse of this claim being also true. Based on this result, it can be proved that the height of such a prime hyperideal is limited by the height of a corresponding quotient hyperideal.
Keywords: Krasner hyperring, prime/maximalhyperideal, Noetherian hyperring, height of a prime hyperideal
Published in RUNG: 01.06.2017; Views: 5512; Downloads: 0
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