Publication detail

Height of hyperideals in Noetherian Krasner hyperrings

BORDBAR, H. CRISTEA, I. NOVÁK, M.

Original Title

Height of hyperideals in Noetherian Krasner hyperrings

Type

journal article in Web of Science

Language

English

Original 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, prime/maximal hyperideal, Noetherian hyperring, height of a prime hyperideal

Authors

BORDBAR, H.; CRISTEA, I.; NOVÁK, M.

Released

1. 6. 2017

ISBN

1223-7027

Periodical

UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS

Year of study

79

Number

2

State

Romania

Pages from

31

Pages to

42

Pages count

12

URL

https://www.scientificbulletin.upb.ro/SeriaA_-_Matematica_si_fizica_aplicate.php#

BibTex

@article{BUT136500,
  author="Hashem {Bordbar} and Irina {Cristea} and Michal {Novák}",
  title="Height of hyperideals in Noetherian Krasner hyperrings",
  journal="UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS",
  year="2017",
  volume="79",
  number="2",
  pages="31--42",
  issn="1223-7027",
  url="https://www.scientificbulletin.upb.ro/SeriaA_-_Matematica_si_fizica_aplicate.php#"
}