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Keywords:
retract; polynomial ring; exponential map
retract; polynomial ring; exponential map
Summary:
Let $A$ be a retract of the polynomial ring in three variables over a field $k$. It is known that if ${\rm char} (k) = 0$ or ${\rm tr.deg}_k A \not = 2$, then $A$ is a polynomial ring. We give some sufficient conditions for $A$ to be the polynomial ring in two variables over $k$ when ${\rm char} (k) > 0$ and ${\rm tr.deg}_k A = 2$.
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