A new construction is given of cyclic semifields of orders $q^{2n}$, $n$ odd, with kernel (left nucleus) $F_{q^n}$ and right and middle nuclei isomorphic to $F_{q^2}$, and the isotopism classes are determined. Furthermore, this construction is generalized to produce potentially new semifields of the same general type that are not isotopic to cyclic semifields. In particular, a new semifield plane of order 45 and new semifield planes of order 165 are constructed by this method
On a generalization of cyclic semifields
MARINO, Giuseppe;POLVERINO, Olga;
2009
Abstract
A new construction is given of cyclic semifields of orders $q^{2n}$, $n$ odd, with kernel (left nucleus) $F_{q^n}$ and right and middle nuclei isomorphic to $F_{q^2}$, and the isotopism classes are determined. Furthermore, this construction is generalized to produce potentially new semifields of the same general type that are not isotopic to cyclic semifields. In particular, a new semifield plane of order 45 and new semifield planes of order 165 are constructed by this methodFile in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.