In the present paper, we will concentrate our efforts on ordered Krasner hyperrings and investigate some of their related properties. Moreover, we introduce and analyze the notion of interior hyperideal in ordered Krasner hyperrings. We also characterize intra-regular ordered Krasner hyperrings by the properties of these interior hyperideals. Finally, we give some results on ordered Krasner hyp...

A Smarandache multi-space is a union of n different spaces equipped with some different structures for an integer n ≥ 2 which can be used both for discrete or connected spaces, particularly for geometries and spacetimes in theoretical physics. In this paper, applying the Smarandaches notion and combining this with hyperrings in hyperring theory, we introduce the notion of multi-hyperring space ...

In this paper, we determine two families R and G of subsets of a hyperring R and sufficient conditions such that two geometric spaces (R,R) and (R,G) are strongly transitive. Moreover, we prove that the relations Γ and α are strongly regular equivalence relations on a hyperfield or a hyperring such that (R,+) has an identity element.

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.

The association between hyperstructures and binary relations had been intensively studied 5,6,10,11,2,4,20 . Chvalina 5,6 and Hort 2 use ordered structures for the construction of semigroups and hypergroups. Rosenberg 4 associated with any binary relation of full domain, a hypergroupoid and found conditions on , such that is a hypergroup. Corsini and Leoreanu 16 study hypergroups and binary rel...

This paper considers the relations among L -fuzzy sets, rough sets and hyperring theory. Based on a complete residuated lattice, the concept of (invertible) L-fuzzy hyperideals of a hyperring is introduced and some related properties are presented. The notions of lower and upper L-fuzzy rough approximation operators with respect to an L-fuzzy hyperideal are provided and some significant propert...

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...