The theory of hyperstructures has been introduced byMarty in 1934 during the 8th Congress of the Scandinavian Mathematicians [4]. Marty introduced the notion of a hypergroup and since then many researchers have worked on this new topic of modern algebra and developed it. The notion of a hyperfield and a hyperring was studied first by Krasner [2] and then some authors followed him, for example, ...

Let R be a commutative hyperring with identity. We introduceand study prime fuzzy hyperideals of R. We investigate the Zariski topologyon FHspec(R), the spectrum of prime fuzzy hyperideals of R.

This paper generalizes the idea of strongly associative hyperoperation introduced in [7]  to the class of hyperrings. We introduce and investigate hyperrings of type 1, type 2 and SDIS. Moreover, we study some examples of these hyperrings and give a new kind of hyperrings called  totally hyperrings. Totally hyperrings give us a characterization of Krasner hyperrings. Also, we investigate these ...

The hyperfield came into being due to a mathematical necessity that appeared during the study of valuation theory fields by M. Krasner, who also defined hyperring, which is related in same way as ring field. and hyperfields, well rings hyperrings, border on each other, it natural problems open questions arise their boundary areas. This paper presents such occasions, more specifically, introduce...

In this paper, we introduce the concept of 1-absorbing prime hyperideals which is an expansion hyperideals. Several properties are provided. For example, it proved that if a strong C-hyperideal I id="M2"> R not prime, then id="M3"> local multiplicative hyperring. Moreover, and study notions primary hyperideals, ...

Let G be an abelian group with identity e. R a graded multiplicative hyperring and ? : Igr(R) expansion function of Igr(R), where is the set all hyperideals R. In this paper, we introduce study concepts ?-primary 2-absorbing which are extended classes prime 2- absorbing R, respectively. Moreover, give basic properties these new types investigate relations among structures.

We apply the classical theory of hyperrings to vague soft sets to derive the concepts of vague soft hyperrings, vague soft hyperideals, and vague soft hyperring homomorphism. The properties and structural characteristics of these concepts are also studied and discussed. Furthermore, the relationship between the concepts introduced here and the corresponding concepts in classical hyperring theor...

In this article we give the definition of weakly prime hyperideals over multiplicative hyperring. We provide important results showing relations between and hyperideals. Then n-hyperideal (1,n) hyperideal hyperrings. investigate their properties some examples. Hyperstructures are very topic because it satisfy to study multidisiplinary. Especially in chemistry, coding theory, geometry, artificia...

In this paper we introduce the notion of composition hyperring. We show that the composition structure of a composition hyperring is determined by a class of its strong multiendomorphisms. Finally, the three isomorphism theorems of ring theory are derived in the context of composition hyperrings.