Superring of Polynomials over a Hyperring
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60162694%3AG43__%2F19%3A00537269" target="_blank" >RIV/60162694:G43__/19:00537269 - isvavai.cz</a>
Result on the web
<a href="https://www.mdpi.com/2227-7390/7/10/902/pdf" target="_blank" >https://www.mdpi.com/2227-7390/7/10/902/pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/math7100902" target="_blank" >10.3390/math7100902</a>
Alternative languages
Result language
angličtina
Original language name
Superring of Polynomials over a Hyperring
Original language description
A Krasner hyperring (for short, a hyperring) is a generalization of a ring such that the addition is multivalued and the multiplication is as usual single valued and satisfies the usual ring properties. One of the important subjects in the theory of hyperrings is the study of polynomials over a hyperring. Recently, polynomials over hyperrings have been studied by Davvaz and Musavi, and they proved that polynomials over a hyperring constitute an additive-multiplicative hyperring that is a hyperstructure in which both addition and multiplication are multivalued and multiplication is distributive with respect to the addition. In this paper, we first show that the polynomials over a hyperring is not an additive-multiplicative hyperring, since the multiplication is not distributive with respect to addition; then, we study hyperideals of polynomials, such as prime and maximal hyperideals and prove that every principal hyperideal generated by an irreducible polynomial is maximal and Hilbert’s basis theorem holds for polynomials over a hyperring.
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
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematics
ISSN
2227-7390
e-ISSN
2227-7390
Volume of the periodical
7
Issue of the periodical within the volume
10
Country of publishing house
CH - SWITZERLAND
Number of pages
15
Pages from-to
902
UT code for WoS article
000498404700031
EID of the result in the Scopus database
2-s2.0-85073770063