Remarks on retracts of polynomial rings in three variables in any characteristic

Let $A$ be a retract of the polynomial ring in three variables over a field $k$. It is known that if $\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{r}(k)=0$ or $\mathrm{t}\mathrm{r}\mathrm{.}\mathrm{d}\mathrm{e}\mathrm{g}{}_{k}A≠2$ then $A$ is a polynomial ring. In this paper, we give some sufficient conditions for $A$ to be the polynomial ring in two variables over $k$ when $\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{r}(k)>0$ and $\mathrm{t}\mathrm{r}\mathrm{.}\mathrm{d}\mathrm{e}\mathrm{g}{}_{k}A=2$.