Height of hyperideals in Noetherian Krasner hyperrings

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F17%3APU123756" target="_blank" >RIV/00216305:26220/17:PU123756 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.scientificbulletin.upb.ro/SeriaA_-_Matematica_si_fizica_aplicate.php#" target="_blank" >https://www.scientificbulletin.upb.ro/SeriaA_-_Matematica_si_fizica_aplicate.php#</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Height of hyperideals in Noetherian Krasner hyperrings

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Height of hyperideals in Noetherian Krasner hyperrings

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

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

ISSN

1223-7027

e-ISSN

—

Svazek periodika

79

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

RO - Rumunsko

Počet stran výsledku

12

Strana od-do

31-42

Kód UT WoS článku

000406126800004

EID výsledku v databázi Scopus

2-s2.0-85020293704