Multiplicative hyperring of fractions and coprime hyperideals

Abstract

In this paper we will introduce the notion of coprime hyperideals in multiplicative hyperrings and we will show some properties of them. Then we introduce the notion of hyperring of fractions generated by a multiplicative hyperring and then we will show some properties of them.

Hyperhomographies on Krasner Hyperfields

“…In the last few years, researchers in the hypercompositional structure theory have investigated, principally from a theoretical point of view, all types of hyperrings: general hyperrings [20], multiplicative hyperrings [15], additive hyperrings [21], superrings [22], but till now, only the Krasner hyperrings have found interesting and useful applications in number theory, algebraic geometry, scheme theory, as mentioned in the introductory part of this article. Here the authors continue the study on the research topic started in [1] about elliptic hypercurves defined on quotient Krasner hyperfield, with applications in cryptography [8].…”

“…The most general one, introduced by Vougiouklis [13], has both addition and multiplication defined as hyperoperations. If only the multiplication is a hyperoperation, then we talk about multiplicative hyperrings [14,15]. If only the addition + is a hyperoperation and the multiplication • is a usual operation, then we say that R is an additive hyperring.…”

Characterizations of Regular Ordered Semigroups by (∈,∈∨(k∗,qk))-Fuzzy Quasi-Ideals

“…For more details on fuzzy ideals and their related notions in ordered semigroups, the reader is referred to [26][27][28][29][30][31][32].…”

Derived Hyperstructures from Hyperconics

“…A special type of additive hyperring is the Krasner's hyperring and hyperfield [20,21,24,27,28]. The construction of different classes of hyperrings can be found in [29][30][31][32][33]. There are different kinds of curves that basically are used in cryptography [34,35].…”