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 |
|---|---|
| Pages (from-to) | 583-604 |
| Journal | Advances in Geometry |
| Volume | 13 |
| Issue number | 4 |
| Publication status | Published - 2013 |
Keywords
- semifield