On the Jacobian conjecture: a new approach via Grobner bases

Abhyankar, Shreeram S. ; Li, Wei (1989) On the Jacobian conjecture: a new approach via Grobner bases Journal of Pure and Applied Algebra, 61 (3). pp. 211-222. ISSN 0022-4049

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/002240...

Related URL: http://dx.doi.org/10.1016/0022-4049(89)90071-6

Abstract

In this paper we propose a new approach to the Jacobian conjecture via the theory of Grobner bases. We give a Grobner base criterion for a polynomial map to be polynomially invertible. Using this and using a result of Bass concerning the inverse degrees of automorphisms of polynomial rings, we reduce the Jacobian conjecture to certain problems in the complexity theory of Grobner bases. As a by-product, we construct examples which show the non-existence of a universal bound of degrees of Grobner bases over a polynomial ring in one variable over a field.

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Deposited On:17 Sep 2010 06:44
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