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1 results

  • POLYNOMIAL ENDOMORPHISMS PRESERVING OUTER RANK IN TWO VARIABLES

  • Part of
  • YONG JIN, XIANKUN DU
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 86 / Issue 2 / October 2012
    Published online by Cambridge University Press:
    16 February 2012, pp. 186-192
    Print publication:
    October 2012
    • Article
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  • An endomorphism φ of a polynomial ring is said to preserve outer rank if φ 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 φ preserving outer rank is an automorphism if one of the following conditions holds: (1) the Jacobian of φ is a nonzero constant; (2) the image of φ contains a coordinate; (3) φ has a ‘fixed point’.