On the kernels of higher $R$-derivations of $R[x_1,\dots,x_n]$

Let $R$ be an integral domain and $A= R[x_1, \dots, x_n]$ be the polynomial ring in $n$ variables. In this article, we study the kernel of higher $R$-derivation $D$ of $A$. It is shown that if $R$ is a HCF ring and $\operatorname{tr.deg}_R(A^D) \leq 1$ then $A^D = R[f]$ for some $f\in A$.