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

Abstract

Let $A$ be a retract of the polynomial ring in three variables over a field $k$. It is known that if $\mathrm{char}(k)=0$ or $tr.deg{}_{k}A\ne 2$ 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 $\mathrm{char}(k)>0$ and $tr.deg{}_{k}A=2$.

14 pages