1. An exponential bound on the number of non-isotopic commutative semifields
- Author
-
Göloğlu, Faruk and Kölsch, Lukas
- Subjects
Computer Science::Systems and Control ,Applied Mathematics ,General Mathematics ,Mathematics::Rings and Algebras ,FOS: Mathematics ,Mathematics - Combinatorics ,Combinatorics (math.CO) ,Commutative Algebra (math.AC) ,Mathematics - Commutative Algebra - Abstract
We show that the number of non-isotopic commutative semifields of odd order $p^{n}$ is exponential in $n$ when $n = 4t$ and $t$ is not a power of $2$. We introduce a new family of commutative semifields and a method for proving isotopy results on commutative semifields that we use to deduce the aforementioned bound. The previous best bound on the number of non-isotopic commutative semifields of odd order was quadratic in $n$ and given by Zhou and Pott [Adv. Math. 234 (2013)]. Similar bounds in the case of even order were given in Kantor [J. Algebra 270 (2003)] and Kantor and Williams [Trans. Amer. Math. Soc. 356 (2004)]., 27 pages. Incorporates reviewer comments. To appear in Transactions of the American Mathematical Society
- Published
- 2022