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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A brief proof of Jacobian hypothesis implies flatness
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by Masayoshi Miyanishi, Lorenzo Robbiano and Stuart Sui Sheng Wang PDF
Proc. Amer. Math. Soc. 109 (1990), 327-330 Request permission

Abstract:

Let $S$ be a polynomial ring in $n$ variables over a field, and let $R$ be the subring generated by $n$ polynomials. We give a short proof of the fact that if the Jacobian determinant of these $n$ polynomials is 1, then $S$ is a flat $R$-module.
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 109 (1990), 327-330
  • MSC: Primary 13F20; Secondary 13B10, 14E07
  • DOI: https://doi.org/10.1090/S0002-9939-1990-1021901-3
  • MathSciNet review: 1021901