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

 

A brief proof of Jacobian hypothesis implies flatness


Authors: Masayoshi Miyanishi, Lorenzo Robbiano and Stuart Sui Sheng Wang
Journal: Proc. Amer. Math. Soc. 109 (1990), 327-330
MSC: Primary 13F20; Secondary 13B10, 14E07
MathSciNet review: 1021901
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1021901-3
PII: S 0002-9939(1990)1021901-3
Keywords: Jacobian conjecture, Jacobian hypothesis, smooth algebra, flat module, regular local ring, regualr system of parameters
Article copyright: © Copyright 1990 American Mathematical Society