Some Results on the Divisible Hyperrings

Abstract

A class of hyperrings known as divisible hyperrings will be studied in this paper. It will be presented as each element in this hyperring is a divisible element. Also shows the relationship between the Jacobsen Radical, and the set of invertible elements and gets some results, and linked these results with the divisible hyperring. After going through the concept of divisible hypermodule that presented by Sopon Boriboon and Sajee Pianskool in 2017, later in 2022 by Hashem Bordbar, and Irina Cristea, the concept of the divisible hyperring will be related to the concept of division hyperring, where each division hyperring is divisible and the converse is achieved under conditions that will be explained in the theorem 3.14. At the end of this paper, it will be clear that the goal of this paper is to study the concept of divisible hyperring by giving some examples, remarks, and results that are related to the concept of divisible hyperrings