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

Hideo Kojima, Takanori Nagamine, Riko Sasagawa

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…