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...

Let k be a p-adic field. It is well-known that k has only finitely many extensions of a given finite degree. In [Kr66], Krasner gives formulae for the number of extensions of a given degree and discriminant. Following his work, we present an algorithm for the computation of generating polynomials for all extensions K/k of a given degree and discriminant.

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...

the concept of algebraic hyperstructures introduced by marty as a generalization of ordinary algebraic structures. in an ordinary algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. the concept of ?-semihyperrings is a generalization of semirings, a generalization of semihyper rings and a generalizat...