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Endomorphisms of the plane sending
linear coordinates to coordinates

Authors: Charles Ching-An Cheng and Arno van den Essen
Journal: Proc. Amer. Math. Soc. 128 (2000), 1911-1915
MSC (1991): Primary 13B25, 13F20, 14E09, 16W20
Published electronically: February 25, 2000
MathSciNet review: 1653437
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Abstract | References | Similar Articles | Additional Information

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 $k[X_{1},X_{2}]$.

References [Enhancements On Off] (What's this?)

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Additional Information

Charles Ching-An Cheng
Affiliation: Department of Mathematics, Oakland University, Rochester, Michigan 48309

Arno van den Essen
Affiliation: Department of Mathematics, University of Nijmegen, Nijmegen, The Netherlands

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
Published electronically: February 25, 2000
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 2000 American Mathematical Society

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