@article{Bordbar2022, 
author = {Hashem Bordbar and Sanja Jančič-Rašovič and Irina Cristea},
title = {Regular local hyperrings and hyperdomains},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {12},
pages = {20767-20780},
keywords = {hyperring, hypermodule, vectorial hyperspace, dimension, regular hyperring, regular parameter element, hyperdomain},
url = {https://www.sciopen.com/article/10.3934/math.20221138},
doi = {10.3934/math.20221138},
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  MM2. 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  R¯=R⟨a⟩, where  a is an element in  M∖M2, and of the regularity of  R¯.}
}