Geodesic
On spectra and minimal polynomials in finite semifields
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 18 (2025) no. 1, pp. 41-50

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We apply the notion of a one-side-ordered minimal polynomial to investigations in finite semifields. A proper finite semifield has non-associative multiplication, that leads to the anomalous properties of its left and right spectra. We obtain the sufficient condition when the right (left) order of a semifield element is a divisor of the multiplicative loop order. The interrelation between the minimal polynomial of non-zero element and its right (left) order is described using the spread set. This relationship fully explains the most interesting and anomalous examples of small-order semifields.
Keywords: semifield, right order, right spectrum, right-ordered minimal polynomial, spread set. 
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Olga V. Kravtsova; Ilya K. Kuzmin. On spectra and minimal polynomials in finite semifields. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 18 (2025) no. 1, pp. 41-50. http://geodesic.mathdoc.fr/item/JSFU_2025_18_1_a4/