Height of hyperideals in Noetherian Krasner hyperrings
The result's identifiers
Result code in 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>
Result on the web
<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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Alternative languages
Result language
angličtina
Original language name
Height of hyperideals in Noetherian Krasner hyperrings
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS
ISSN
1223-7027
e-ISSN
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Volume of the periodical
79
Issue of the periodical within the volume
2
Country of publishing house
RO - ROMANIA
Number of pages
12
Pages from-to
31-42
UT code for WoS article
000406126800004
EID of the result in the Scopus database
2-s2.0-85020293704