On the nuclei of a finite semifield (Q2869133)

A semifield is an algebra satisfying the axioms for a skewfield except that the multiplication may not be associative. One geometric use of semifields is to coordinatize semifield planes. The left, right and middle nuclei are defined as the sets of elements for which the equation \((a*b)*c = a*(b*c)\) holds for all possibilities of the other two variables. The center consists of all elements in the intersection of the three nuclei that commute with the elements of the semifield. The authors describe and improve the techniques for calculating these nuclei of a semifield and use these techniques to determine the order of the nuclei and center of some commutative presemifields of odd characteristic.NEWLINENEWLINEFor the entire collection see [Zbl 1253.00023].