Superring of Polynomials over a Hyperring
Identifikátory výsledku
Kód výsledku v 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>
Výsledek na webu
<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>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Superring of Polynomials over a Hyperring
Popis výsledku v původním jazyce
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.
Název v anglickém jazyce
Superring of Polynomials over a Hyperring
Popis výsledku anglicky
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.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10101 - Pure mathematics
Návaznosti výsledku
Projekt
—
Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Ostatní
Rok uplatnění
2019
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Mathematics
ISSN
2227-7390
e-ISSN
2227-7390
Svazek periodika
7
Číslo periodika v rámci svazku
10
Stát vydavatele periodika
CH - Švýcarská konfederace
Počet stran výsledku
15
Strana od-do
902
Kód UT WoS článku
000498404700031
EID výsledku v databázi Scopus
2-s2.0-85073770063