Indexed on: 03 Jan '16Published on: 03 Jan '16Published in: Mathematics - Commutative Algebra
In this paper we present an equivalent statement to the Jacobian conjecture. For a polynomial map F on an affine space of dimension n, we define recursively n finite sequences of polynomials. We give an equivalent condition to the invertibility of F as well as a formula for the inverse of F in terms of these finite sequences of polynomials. Some examples illustrate the effective aspects of our approach.