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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 resultstates 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 knownresults of A. Nowicki on commutative bases of derivations.

Simplicity and Commutative Bases of Derivations in Polynomial and Power Series Rings