| Autor: |
Hashem Bordbar, Sanja Jančič-Rašovič, Irina Cristea |
| Jazyk: |
angličtina |
| Rok vydání: |
2022 |
| Předmět: |
|
| Zdroj: |
AIMS Mathematics, Vol 7, Iss 12, Pp 20767-20780 (2022) |
| Druh dokumentu: |
article |
| ISSN: |
2473-6988 |
| DOI: |
10.3934/math.20221138?viewType=HTML |
| Popis: |
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 $ \frac{M}{M^2} $. The aim of the paper is to show that any regular local hyperring is a hyperdomain. 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 $ \overline{R} = \frac{R}{\langle a\rangle} $, where $ a $ is an element in $ M\setminus M^2 $, and of the regularity of $ \overline{R} $. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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