| Title: | HEIGHT OF HYPERIDEALS IN NOETHERIAN KRASNER HYPERRINGS |
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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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| Files: |
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| Language: | English |
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| Work type: | Not categorized |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | UNG - University of Nova Gorica
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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. |
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| Keywords: | Krasner hyperring, prime/maximalhyperideal, Noetherian hyperring, height of a prime hyperideal |
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| Publication version: | Version of Record |
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| Year of publishing: | 2017 |
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| Number of pages: | 31-42 |
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| Numbering: | 2, 79 |
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| PID: | 20.500.12556/RUNG-3106-eea6aff8-499f-20b3-44f1-8929aa52e57a |
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| COBISS.SI-ID: | 4790011 |
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| NUK URN: | URN:SI:UNG:REP:M8RDASFO |
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| Publication date in RUNG: | 01.06.2017 |
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| Views: | 5564 |
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| Downloads: | 0 |
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