ON RELATIONS BETWEEN JACOBIANS AND MINIMAL POLYNOMIALS

We give some relations between Jacobians and minimal polynomials of n polynomials in n variables, which yield some new effective criteria to decide whether a polynomial or a rational map is invertible, and to c alculate the inverse if it exists. Our new criteria work for all ratio nal maps from K-n to K-n, where K is an arbitrary field. We also formu late a conjecture, which is equivalent to the Jacobian conjecture.