  Skew polynomial rings were used to construct finite semifields by Petit in
1966, following from a construction of Ore and Jacobson of associative division
algebras. In 1989 Jha and Johnson constructed the so-called cyclic semifields,
obtained using irreducible semilinear transformations. In this work we show
that these two constructions in fact lead to isotopic semifields, 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 2008 and implicitly in recent work by
Dempwolff.
