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1.
Overview on the height of a hyperideal in Krasner hyperrings
Hashem Bordbar, Irina Elena Cristea, Michal Novak, 2017, published scientific conference contribution abstract

Keywords: Krasner hyperring, prime hyperideal, Noetherian hyperring
Published in RUNG: 30.08.2017; Views: 3864; Downloads: 0
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2.
HEIGHT OF HYPERIDEALS IN NOETHERIAN KRASNER HYPERRINGS
Hashem Bordbar, Irina Elena Cristea, Michal Novak, 2017, original scientific article

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: 4657; Downloads: 0
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