| Title: | Regular local hyperrings and hyperdomains |
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| Authors: | ID Bordbar, Hashem, University of Nova Gorica (Author)
ID Cristea, Irina Elena, University of Nova Gorica (Author)
ID Rasovic, Sanja, University of Montenegro (Author) |
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| Files: |  10.3934_math.20221138.pdf (258,07 KB)
MD5: 65B2C2A7C3858B1F7795FC2051105637
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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: | This paper falls in the area of hypercompositional algebra. In particular, it focuses on the
class of Krasner hyperrings and it studies the regular local hyperrings. These are Krasner hyperrings R with a unique maximal hyperideal M having the dimension equal to the dimension of the vectorial hyperspace M. The aim of the paper is to show that any regular local hyperring is a hyperdomain. M2 For proving this, we make use of the relationship existing between the dimension of the vectorial hyperspaces related to the hyperring R and to the quotient hyperring R = R , where a is an element in M \ M2, and of the regularity of R. |
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| Keywords: | hyperring, hypermodule, vectorialhyperspace, dimension, regularhyperring, regular parameter element, hyperdomain |
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| Publication version: | Version of Record |
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| Year of publishing: | 2022 |
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| Number of pages: | 20767-20780 |
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| Numbering: | 12, 7 |
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| PID: | 20.500.12556/RUNG-7630  |
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| COBISS.SI-ID: | 123160323 |
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| DOI: | https://doi.org/10.3934/math.20221138 |
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| NUK URN: | URN:SI:UNG:REP:YVRIZZNJ |
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| Publication date in RUNG: | 27.09.2022 |
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| Views: | 1062 |
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| Downloads: | 21 |
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