Open AccessA Note on the Jacobian Conjecture
Author(s) -
Zhili Zhang
Publication year - 1990
Publication title -
daimi pb
Language(s) - English
Resource type - Journals
eISSN - 2245-9316
pISSN - 0105-8517
DOI - 10.7146/dpb.v19i303.6696
Subject(s) - corollary , jacobian matrix and determinant , mathematics , conjecture , inverse , homogeneous , degree (music) , polynomial , combinatorics , mathematical analysis , geometry , physics , acoustics
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.