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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2024 MCQ for Journal of the American Mathematical Society is 4.83.

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The tame and the wild automorphisms of polynomial rings in three variables
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by Ivan P. Shestakov and Ualbai U. Umirbaev;
J. Amer. Math. Soc. 17 (2004), 197-227
DOI: https://doi.org/10.1090/S0894-0347-03-00440-5
Published electronically: October 3, 2003

Abstract:

A characterization of tame automorphisms of the algebra $A=F[x_1,x_2,x_3]$ of polynomials in three variables over a field $F$ of characteristic $0$ is obtained. In particular, it is proved that the well-known Nagata automorphism is wild. It is also proved that the tame and the wild automorphisms of $A$ are algorithmically recognizable.
References
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Bibliographic Information
  • Ivan P. Shestakov
  • Affiliation: Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, São Paulo - SP, 05311–970, Brazil; Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia
  • MR Author ID: 289548
  • Email: shestak@ime.usp.br
  • Ualbai U. Umirbaev
  • Affiliation: Department of Mathematics, Eurasian National University, Astana, 473021, Kazakhstan
  • Email: umirbaev@yahoo.com
  • Received by editor(s): January 8, 2003
  • Published electronically: October 3, 2003
  • Additional Notes: The first author was supported by CNPq.
    The second author was supported by the FAPESP Proc.00/06832-8.
  • © Copyright 2003 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 17 (2004), 197-227
  • MSC (2000): Primary 13F20, 13P10, 14H37; Secondary 14R10, 14R15
  • DOI: https://doi.org/10.1090/S0894-0347-03-00440-5
  • MathSciNet review: 2015334