The BEL-rank of finite semifields

TL;DR

This paper introduces the BEL-rank as a new invariant for finite semifields, providing geometric and algebraic interpretations, an efficient calculation method, and computational results for small cases.

Contribution

It defines the BEL-rank, proves its invariance under isotopism, and offers practical computation techniques along with initial data for small semifields.

Findings

BEL-rank is an isotopism invariant

Provides geometric and algebraic interpretations

Includes an efficient calculation method

Abstract

In this article we introduce the notion of the BEL-rank of a finite semifield, prove that it is an invariant for the isotopism classes, and give geometric and algebraic interpretations of this new invariant. Moreover, we describe an efficient method for calculating the BEL-rank, and present computational results for all known small semifields.