On the nuclei of a finite semifield

TL;DR

This paper enhances techniques for calculating nuclei of semifields and applies these methods to determine the order of nuclei and centers in certain commutative presemifields of odd characteristic.

Contribution

It introduces improved methods for computing nuclei and applies them to specific classes of commutative presemifields, advancing understanding of their algebraic structure.

Findings

Determined the order of nuclei in selected presemifields

Calculated the center of these presemifields

Provided new insights into their algebraic properties

Abstract

In this paper we collect and improve the techniques for calculating the nuclei of a semifield and we use these tools to determine the order of the nuclei and of the center of some commutative presemifields of odd characteristic recently constructed.