  The first part of the paper will describe a recent result of K. Retert in
(\cite{Ret}) for $k[x_1,\ldots,x_n]$ and $k[[x_1,\ldots,x_n]]$. This result
states that if $\mathfrak{D}$ is a set of commute $k$-derivations of $k[x,y]$
such that both $\partial_x \in \mathfrak{D}$ and the ring is
$\mathfrak{D}$-simple, then there is $d \in \mathfrak{D}$ such that $k[x,y]$ is
$\{\partial_x,d\}$-simple. As applications, we obtain relationships with known
results of A. Nowicki on commutative bases of derivations.
