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Proceedings of the American Mathematical Society

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Eulerian operators and the Jacobian conjecture


Author: Arno van den Essen
Journal: Proc. Amer. Math. Soc. 118 (1993), 373-378
MSC: Primary 14E07; Secondary 13B10, 13H10, 14E20, 16S30, 16S32
MathSciNet review: 1129883
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Abstract: In this paper we introduce a new class of polynomial maps, the so-called nice polynomial maps. Using Eulerian operators we show how for these polynomial maps the main results obtained by Bass (Differential structure of étale extensions of polynomial algebras, Proc. Workshop on Commutative Algebra, MSRI, 1987) can be proved in a very simple and elementary way. Furthermore we show that every polynomial map $ F$ satisfying the Jacobian condition, det $ JF \in {k^{\ast}}$, is equivalent to a nice polynomial map; more precisely the polynomial map $ {F_{(\lambda )}}(X) = F(X + \lambda ) - F(\lambda )$ is nice for almost all $ \lambda \in {k^n}$.


References [Enhancements On Off] (What's this?)

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  • [2] Kossivi Adjamagbo and Arno van den Essen, Eulerian systems of partial differential equations and the Jacobian conjecture, J. Pure Appl. Algebra 74 (1991), no. 1, 1–15. MR 1129126, 10.1016/0022-4049(91)90045-4
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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1129883-3
Article copyright: © Copyright 1993 American Mathematical Society