  In this paper we present a theorem concerning an equivalent statement of the
Jacobian Conjecture in terms of Picard-Vessiot extensions. Our theorem
completes the earlier work of T. Crespo and Z. Hajto which suggested an
effective criterion for detecting polynomial automorphisms of affine spaces. We
show a simplified criterion and give a bound on the number of wronskians
determinants which we need to consider in order to check if a given polynomial
mapping with non-zero constant Jacobian determinant is a polynomial
automorphism. Our method is specially efficient with cubic homogeneous mappings
introduced and studied in fundamental papers by H. Bass, E. Connell, D. Wright
and L. Druzkowski.

Commutative Algebra