## Abstract

Skew polynomial rings were used to construct fi nite semifi elds by

Petit in [20], following from a construction of Ore and Jacobson of associative

division algebras. Johnson and Jha [10] later constructed the so-called cyclic

semif ields, obtained using irreducible semilinear transformations. In this work

we show that these two constructions in fact lead to isotopic semifi elds, show

how the skew polynomial construction can be used to calculate the nuclei

more easily, and provide an upper bound for the number of isotopism classes,

improving the bounds obtained by Kantor and Liebler in [13] and implicitly

by Dempwolff in [2].

Petit in [20], following from a construction of Ore and Jacobson of associative

division algebras. Johnson and Jha [10] later constructed the so-called cyclic

semif ields, obtained using irreducible semilinear transformations. In this work

we show that these two constructions in fact lead to isotopic semifi elds, show

how the skew polynomial construction can be used to calculate the nuclei

more easily, and provide an upper bound for the number of isotopism classes,

improving the bounds obtained by Kantor and Liebler in [13] and implicitly

by Dempwolff in [2].

Original language | English |
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Pages (from-to) | 583-604 |

Journal | Advances in Geometry |

Volume | 13 |

Issue number | 4 |

Publication status | Published - 2013 |

## Keywords

- semifield