A Note on the Jacobian Conjecture

Abstract

We extend a corollary in H. Bass, et al.: The Jacobian Conjecture: Reduction of Degree and Formal Expansion of the Inverse, 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 f_i = x_i-h_i, where h_i is homogeneous of degree >= 2, i = 1,2.