In this note we introduce a new equivalence relation θ∗ on a (semi)hyperring R and we show that it is strongly regular. Also we prove that, R/θ∗, the equivalence class of this equivalence relation under usual operations consists a commutative (semi-)ring. Finally we introduce the notion of θ-parts of hyperrings and investigate the important properties of them. Mathematics Subject Classification...

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...

The basis of this study, which was put forth in order to appropriate a special area the hyperring theory, has recently been studied as generalization ring uses module theory an application field, is based on integrally closed Krasner hyperrings and (almost) integral dependence applications krasner hyperrings.

In this paper, our aim is to introduce the notion of a composition (m,n, k)-hyperring and to analyze its properties. We also consider the algebraic structure of (m,n, k) hyperrings which is a generalization of composition rings and composition hyperrings. Also, the isomorphism theorems of ring theory are derived in the context of composition (m,n, k)-hyperrings.

the concept of  -semihyperring is a generalization of semiring, a generalization of semihyperring and a generalization of      -semiring. since the theory of ideals plays an important role in the theory of  - semihyperring, in this paper, we will make an intensive study of the notions of noetherian, artinian, simple and   regular      -semihyperrings. the bulk of this paper...

Based on the concepts of composition ring and composition hyperring, in this note we introduce the notion of composition structure for (m,n)-hyperrings and study the connections with composition hyperrings. Moreover we show that particular strong endomorphisms of (m,n)-hyperrings can determine the composition structure of a such (m,n)-hyperrings. Finally, the three isomorphism theorems are pres...