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A Contribution to Keller’s Jacobian Conjecture II

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Deformations of Mathematical Structures

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Summary

In this paper we give two necessary and sufficient conditions for a complex polynomial Q in two variables x,y to exist, such that PxQy - PyQx = 1 holds for the given analogous polynomial P.

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References

  1. S.S. Abhyankar, Expansion technique in algebraic geometry, Tata Institute of Fundamental Research, Bombay, 1977.

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  2. H. Bass, E.H. Connel and D. Wright, ‘The Jacobian conjecture; reduction of degree and formal expansion of the inverse’, Bull, of Amer. Math. Soc. 7, No. 2, (1982), pp.287–330.

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  3. Z. Charzyński, J. Chąrzyński and P. Skibinski, ‘A contribution to Keller’s Jacobian conjecture’, Seminar on Deformations, Proceedings, Łódź-Warsaw 1982/84, Lecture Notes in Math. 1165, pp.36–51, Springer-Verlag, Berlin — Heidelberg, 1985.

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  4. Z. Charzyński and P. Skibiński, ‘A criterion for explicit dependence of polynomials’, Bull. Soc. Sci. Lettres Łódź (to appear).

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  5. O. H. Keller, ‘Ganze Cremona-Transformationen’, Monats. Math. Physik 47 (1939), pp.299–306.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Łódź University, ul. S. Banacha 22, 90-238, Łódź, Poland

    Zygmunt Charzyński, Jacek Chądzyński & Przemysław Skibiński

Authors
  1. Zygmunt Charzyński
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  2. Jacek Chądzyński
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  3. Przemysław Skibiński
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Editor information

Editors and Affiliations

  1. Institute of Mathematics of the Polish Academy of Sciences, Łódź, Poland

    Julian Ławrynowicz

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© 1989 Kluwer Academic Publishers

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Charzyński, Z., Chądzyński, J., Skibiński, P. (1989). A Contribution to Keller’s Jacobian Conjecture II. In: Ławrynowicz, J. (eds) Deformations of Mathematical Structures. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2643-1_12

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  • DOI: https://doi.org/10.1007/978-94-009-2643-1_12

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7693-7

  • Online ISBN: 978-94-009-2643-1

  • eBook Packages: Springer Book Archive

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