| Title: | HEIGHT OF HYPERIDEALS IN NOETHERIAN KRASNER HYPERRINGS |
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| Authors: | Bordbar, Hashem (Author)
Cristea, Irina (Author)
Novak, Michal (Author) |
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| Files: | This document has no files. This document may have a phisical copy in the library of the organization, check the status via COBISS.  |
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| Language: | English |
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| Work type: | Not categorized (r6) |
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| Tipology: | 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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| Year of publishing: | 2017 |
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| Number of pages: | 31-42 |
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| Numbering: | 79, 2 |
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| COBISS_ID: | 4790011 |
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| URN: | URN:SI:UNG:REP:M8RDASFO |
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| Views: | 3660 |
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| Downloads: | 0 |
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| Metadata: |     |
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| Categories: | Document is not linked to any category. |
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