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On the jacobian equation J(f, g) = 0 for Polynomials in k[x, y]

Published online by Cambridge University Press:  22 January 2016

Andrzej Nowicki
Andrzej Nowicki*
Affiliation:
Institute of Mathematics, N. Copernicus University, ul. Chopina 12/18, 87-100 Torun, Poland, and Department of Mathematics, Shinshu University, 390 Matsumoto, Japan
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Let k[x, y] be the ring of polynomials in two variables over a field k of characteristic zero.

If f, g ∈ k[x, y] then we write f ~ g in the case where f = ag, for some a ∈ k = k\{0}, and we denote by [f, g] the jacobian of (f, g), that is, [f, g] = fxgy - fygx

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 109 , March 1988 , pp. 151 - 157
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1988

References

[1] Abhyankar, S. S., Expansion Techniques in Algebraic Geometry, Tata Institute of Fundamental Research, Bombay, 1977.Google Scholar
[1] Appelgate, H. and Onishi, H., The Jacobian conjecture in two variables, J. Pure Appl. Algebra, 37 (1985), 215–227.CrossRefGoogle Scholar
[1] Nakai, Y. and Baba, K., A generalization of Magnus’ theorem, Osaka J. Math., 14 (1977), 403–409.Google Scholar
[1] Nousiainen, P. and Sweedler, M. E., Automorphisms of polynomial and power series rings, J. Pure Appl. Algebra, 29 (1983), 93–97.CrossRefGoogle Scholar
[1] Nowicki, A., On the Jacobian conjecture in two variables, to appear.Google Scholar
[1] Nowicki, A. and Nagata, M., Rings of constants for k-derivations in k[x 1 …, xn] , to appear.Google Scholar
[1] Nowicki, A. and Nakai, Y., On Appelgate-Onishi’s lemmas, to appear.Google Scholar