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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


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