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 method
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11591/194759
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