Commutative quasigroups and semifields from planar functions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10489471" target="_blank" >RIV/00216208:11320/24:10489471 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=7p3tISuAsh" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=7p3tISuAsh</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1080/00927872.2023.2275392" target="_blank" >10.1080/00927872.2023.2275392</a>

Result language
angličtina
Original language name
Commutative quasigroups and semifields from planar functions
Original language description
Finite commutative semifields of odd characteristic correspond to Dembowski-Ostrom polynomials. A new proof of this fact is the main result of this paper. The paper also discusses strong isotopy of commutative semifields and shows that the limit on the number of strong isotopy classes can be obtained from a general theorem on commutative loops. By this theorem for each commutative loop Q the commutative isotopes form at most |N mu:(N-mu)N-2(lambda)| classes with respect to the strong isotopy, where N mu and N lambda are the middle and the left nucleus of Q. Loops Q(1) and Q(2) are said to be strongly isotopic if there exists an isotopism Q(1) -> Q(2) of the form (alpha,alpha,gamma).
Czech name
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Czech description
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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

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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