An M-polysymmetrical hyperring $(R,+,cdot )$ is an algebraic system, where $(R,+)$ is an M-polysymmetrical hypergroup, $(R,cdot )$ is a semigroup and $cdot$ is bilaterally distributive over $+$. In this paper, we introduce the concept of hyperideals of an M-polysymmetrical hyperring and by using this concept, we construct an ordinary quotient ring. Finally, the fundamental theorem of homomorphi...

In this paper, our aim is to generalize and extend the Hopkins-Levitzki theorem from noncommutative rings Krasner hyperring. Also, we prove that a hyperring R Noetherian if only it satisfies ascending chain conditions of prime hyperideals.

A class of hyperrings known as divisible will be studied in this paper. It presented each element hyperring is a element. Also shows the relationship between Jacobsen Radical, and set invertible elements gets some results, linked these results with hyperring. After going through concept hypermodule that by Sopon Boriboon Sajee Pianskool 2017, later 2022 Hashem Bordbar, Irina Cristea, related to...

Let G be a group (monoid) with identity e and R commutative Krasner hyperring. In this paper, we introduce the concepts of graded absorbing hyperideals hyperring such as, 2-absorbing hyperideals, n-absorbing subhypermodules. Some basic properties these structures characterizations homogeneous components are proved.

In the theory of hyperrings, fundamental relations make a connection between hyperrings and ordinary rings. Commutative fundamental rings and the fundamental relation α which is the smallest strongly regular relation in hyperringswere introduced by Davvaz and Vougiouklis (2007). Recently, another strongly regular relation named θ on hyperrings has been studied by Ameri and Norouzi (2013). Ameri...

This survey article presents some recent results in the theory of hyperfields and hyperrings, algebraic structures for which the "sum" of two elements is a subset of the structure. The results in this paper show that these structures .cannot always be embedded in the decomposition of an ordinary structure (ring or field) in equivalence classes and that the structural results for hyperfields and...

In this paper we introduce the concept of Krasner hyperring $(R,+,cdot)$together with a suitable partial order relation $le $.xle y$.  Also we consider some Krasner hyperrings and define a binary relation on them such that to become ordered Krasner hyperrings. By using the notion of pseudoorder on an ordered Krasner hyperring $(R,+,cdot,le)$, we obtain an ordered ring. Moreover, we study s...