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...

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...

$!!!!$ In this paper, the notion of fuzzy $!$ Krasner $!(m, n)$-hyperrings($!F^{(m, n)}!$-hyperrings) by using the notion of$F^m$-hyperoperations and $F^n$-operations is introduced and somerelated properties are investigated. In this regards,relationships between Krasner $F^{(m, n)}$-hyperrings and Krasner$(m, n)$-hyperrings are considered. We shall prove that everyKrasner $F^{(m, n)}$-hyperrin...

$!!!!$ in this paper, the notion of fuzzy $!$ krasner $!(m, n)$-hyperrings($!f^{(m, n)}!$-hyperrings) by using the notion of$f^m$-hyperoperations and $f^n$-operations is introduced and somerelated properties are investigated. in this regards,relationships between krasner $f^{(m, n)}$-hyperrings and krasner$(m, n)$-hyperrings are considered. we shall prove that everykrasner $f^{(m, n)}$-hyperrin...

Inspired by the classical concept of height of a prime ideal in a ring, we proposed in a precedent paper the notion of height of a prime hyperideal in a Krasner hyperring. In this note we first generalize some results concerning the height of a prime hyperideal in a Noetherian Krasner hyperring, with the intent to extend this definition to the case of a general hyperideal in a such hyperring. T...

in this paper, we introduce the notion of derivation on krasner hyperrings as follows: the function d : r  r isa derivation on a krasner hyperring r if for all , , ry x  ) ( ) ( = ) ( y d x d y x d   andd (x  y) d (x)  y  x  d ( y). then, we investigate some fundamental properties of derivation on krasnerhyperings and prime krasner hyperrings. also, we introduce differential krasner hy...

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.