Polynomial endomorphisms preserving outer rank in two variables

Authors

  • yong Jin

Keywords:

outer rank, coordinate, test polynomial, retract

Abstract

An endomorphism $\varphi$ of a polynomial ring is called preserving outer rank if $\varphi$ sends each polynomial to one with the same outer rank. For the polynomial ring in two variables over a field of characteristic $0$ we prove that an endomorphism $\varphi$ preserving outer rank is an automorphism if one of the following conditions holds: (1) The Jacobian of $\varphi$ is a non-zero constant; (2) The image of $\varphi$ contains a coordinate; (3) $\varphi$ has a ``fixed point". DOI: 10.1017/S0004972712000044

Published

2012-08-27

Issue

Vol. 86 No. 2 (2012)

Section

Articles
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