Note on Jacobian Conjecture

We extend a corollary in [2], yielding a sufficient and necessary condition for a polynomial map to have an inverse of the simplest form, and give a surprisingly simple proof for the Jacobian Conjecture in two variables of the case fi = xi − hi, where hi is homogeneous of degree ≥ 2, i = 1, 2. 1 The Jacobian conjecture Let k be a fiels of characteristic 0, and let f = (f1,..., fn) be a polynomial map from kn to kn, fi ∈ k[x1,..., xn], 1 ≤ i ≤ n. The Jacobian matrix for f is: J(f)