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arXiv · 2412.13424

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

Hideo Kojima·Takanori Nagamine·Riko Sasagawa
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Abstract

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. In this paper, 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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Hideo Kojima, Takanori Nagamine, Riko Sasagawa. 2024-12-18. Remarks on retracts of polynomial rings in three variables in any characteristic. https://arxiv.org/abs/2412.13424

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