Coordinates, retracts and automorphisms

Yun-Chang Li

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arXiv · 1206.5085

Coordinates, retracts and automorphisms

Yun-Chang Li

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Abstract

Let $K$ be a field of characteristic zero, $K[x,y]$ be the polynomial ring in two variables. Let $ϕ=(f, g)$ be an endomorphism of $K[x,y]$. It is proved that if $ϕ$ maps each coordinate to a generator of some proper retract, then it is an automorphism. As a corollary, the retract preserving problem is solved for both polynomial ring over $K$ and free algebra over an arbitrary field when $n=2$.

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BibTeX RIS

Yun-Chang Li. 2012-06-22. Coordinates, retracts and automorphisms. https://arxiv.org/abs/1206.5085

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