Height of hyperideals in Noetherian Krasner hyperrings

Hashem Bordbar (Author), Irina Cristea (Author), Michal Novák (Author)

Abstract

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.

Keywords

Krasner hyperring;Noetherian hyperring;prime hyperideals;

Data

Language:	English
Year of publishing:	2017
Typology:	1.01 - Original Scientific Article
Organization:	UNG - University of Nova Gorica
UDC:	510.6
COBISS:	4790011
ISSN:	1223-7027
Views:	3793
Downloads:	0
Average score:	0 (0 votes)
Metadata:

Other data

URN:	URN:SI:UNG
Type (COBISS):	Not categorized
Pages:	str. 31-42
Volume:	ǂVol. ǂ79
Issue:	ǂiss. ǂ2
Chronology:	2017
ID:	10838336