On relations between Jacobians and minimal polynomials

Abstract 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 calculate the inverse if it exists. Our new criteria work for all rational maps from K n to K n , where K is an arbitrary field. We also formulate a conjecture, which is equivalent to the Jacobian conjecture.