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

článek v časopise ve Web of Science, Jimp

Language

angličtina

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

Rumunsko

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#"
}