Detail publikačního výsledku

Height of hyperideals in Noetherian Krasner hyperrings

BORDBAR, H.; CRISTEA, I.; NOVÁK, M.

Originální název

Height of hyperideals in Noetherian Krasner hyperrings

Anglický název

Height of hyperideals in Noetherian Krasner hyperrings

Druh

Článek WoS

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

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

Klíčová slova v angličtině

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

Autoři

BORDBAR, H.; CRISTEA, I.; NOVÁK, M.

Rok RIV

2018

Vydáno

01.06.2017

ISSN

1223-7027

Periodikum

University Politehnica of Bucharest Scientific Bulletin-Series A-Applied Mathematics and Physics

Svazek

79

Číslo

2

Stát

Rumunsko

Strany od

31

Strany do

42

Strany počet

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#"
}