A note on generalized distributive sets of a finite Dickson nearfield

Let $\mathbb{F}_{q^n}$ be a finite field where $q=p^l$ ($p$ is a prime) and a Dickson nearfield $R$ associated to the field. In this note we investigate the basic properties of the generalized distributive set $D(a,b)$ where $a,b\in R$. The set is well-known when $n=1, 2$. For $n>2$, we characterize