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Endomorphisms of the plane sending linear coordinates to coordinates

Author(s): Charles Ching-An Cheng; Arno van den Essen
Journal: Proc. Amer. Math. Soc. 128 (2000), 1911-1915.
MSC (1991): Primary 13B25, 13F20, 14E09, 16W20
Posted: February 25, 2000
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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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Additional Information:

Charles Ching-An Cheng
Affiliation: Department of Mathematics, Oakland University, Rochester, Michigan 48309
Email: cheng@oakland.edu

Arno van den Essen
Affiliation: Department of Mathematics, University of Nijmegen, Nijmegen, The Netherlands
Email: essen@sci.kun.nl

DOI: 10.1090/S0002-9939-00-05236-9
PII: S 0002-9939(00)05236-9
Keywords: Jacobian conjecture, automorphism, endomorphism, derivation, algebraically closed field, coordinate
Received by editor(s): December 12, 1997
Received by editor(s) in revised form: September 1, 1998
Posted: February 25, 2000
Communicated by: Wolmer V. Vasconcelos
Copyright of article: Copyright 2000, American Mathematical Society

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