Geodesic
On a generalization of cyclic semifields
Journal of Algebraic Combinatorics, Tome 29 (2009) no. 1, pp. 1-34.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: A new construction is given of cyclic semifields of orders $q ^{2 n }, n$ odd, with kernel (left nucleus) $\mathbb F _{ q $^ n mathbbF_q^n and right and middle nuclei isomorphic to $\mathbb F _{ q $^2 mathbbF_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 $4 ^{5}$ and new semifield planes of order $16 ^{5}$ are constructed by this method.
Keywords: keywords cyclic semifield, net replacement, lifting 
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Johnson, Norman L.; Marino, Giuseppe; Polverino, Olga; Trombetti, Rocco. On a generalization of cyclic semifields. Journal of Algebraic Combinatorics, Tome 29 (2009) no. 1, pp. 1-34. http://geodesic.mathdoc.fr/item/JAC_2009__29_1_a5/