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Authors:ID Bordbar, Hashem, Shahid Bahonar University, Iran (Author)
ID Cristea, Irina Elena, University of Nova Gorica, Slovenia (Author)
ID Novak, Michal, Brno University of Technology, Czech Republic (Author)
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Work type:Not categorized
Typology: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
Publication version:Version of Record
Year of publishing:2017
Number of pages:31-42
Numbering:2, 79
PID:20.500.12556/RUNG-3106-eea6aff8-499f-20b3-44f1-8929aa52e57a New window
COBISS.SI-ID:4790011 New window
Publication date in RUNG:01.06.2017
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Title:U.P.B. Scientific Bulletin, Series A
Year of publishing:2017