Research article

Regular local hyperrings and hyperdomains

  • Received: 14 July 2022 Revised: 09 September 2022 Accepted: 14 September 2022 Published: 26 September 2022
  • MSC : 20N20, 13E05

  • 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} $.

    Citation: Hashem Bordbar, Sanja Jančič-Rašovič, Irina Cristea. Regular local hyperrings and hyperdomains[J]. AIMS Mathematics, 2022, 7(12): 20767-20780. doi: 10.3934/math.20221138

    Related Papers:

  • 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} $.



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