Height of Hyperideals in Noetherian Krasner Hyperrings
نویسندگان
چکیده
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. The main results in this note show that, in a commutative Noetherian Krasner hyperring, the height of a minimal prime hyperideal over a proper hyperideal generated by n elements is less than or equal to n, the converse of this claim being also true. Based on this result, it can be proved that the height of such a prime hyperideal is limited by the height of a corresponding quotient hyperideal.
منابع مشابه
Operations on hyperideals in ordered Krasner hyperrings
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...
متن کاملKrasner $F^{(m, n)}$-Hyperrings
$!!!!$ 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...
متن کاملOn graded hyperrings and graded hypermodules
Let $G$ be a monoid with identity $e$. In this paper, first we introduce the notions of $G$-graded hyperrings, graded hyperideals and graded hyperfields in the sense of Krasner hyperring $R$. Also, we define the notion of a greded $R$-hypermodules and some examples are presented. Then we investigate graded maximal, graded prime and graded primary hyperideals of a graded hyperring $R$. Finally, ...
متن کاملOrdered Krasner Hyperrings
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...
متن کاملPrime Hyperideal in Multiplicative Ternary Hyperrings
In the year 1971, W. G. Lister [14] introduced the notion of ternary ring. Later in the year 2014, J. R. Castillo and Jocelyn S. ParaderoVilela [2] introduced the notion of krasner ternary hyperring. In [6] we introduce the notion of multiplicative ternary hyperring. In this paper we study prime hyperideals in a multiplicative ternary hyperring. We obtain some Characterizations of prime hyperid...
متن کامل