Endomorphisms of the plane sending linear coordinates to coordinates

Cheng, Charles; van den Essen, Arno

doi:10.1090/S0002-9939-00-05236-9

Endomorphisms of the plane sending linear coordinates to coordinates
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by Charles Ching-An Cheng and Arno van den Essen PDF

Proc. Amer. Math. Soc. 128 (2000), 1911-1915 Request permission

Abstract:

Let $k$ be a field of characteristic zero. We show that an endomorphism of $k[X_{1},X_{2}]$ which sends each linear coordinate to a coordinate is an automorphism of $k[X_{1},X_{2}]$.

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