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Authors:Bordbar, Hashem (Author)
Cristea, Irina (Author)
Novak, Michal (Author)
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Work type:Not categorized (r6)
Tipology:1.01 - Original Scientific Article
Organization:UNG - University of Nova Gorica
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
Year of publishing:2017
Number of pages:31-42
Numbering:79, 2
COBISS_ID:4790011 Link is opened in a new window
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Title:U.P.B. Scientific Bulletin, Series A
Year of publishing:2017