On relations between Jacobians and minimal polynomials Original Research Article

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 Kn to Kn, where K is an arbitrary field. We also formulate a conjecture, which is equivalent to the Jacobian conjecture.