  We prove that a polynomial map is invertible if and only if some associated
differential ring homomorphism is bijective. To this end, we use a theorem of
Crespo and Hajto linking the invertibility of polynomial maps with
Picard-Vessiot extensions of partial differential fields, the theory of
strongly normal extensions as presented by Kovacic and the characterization of
Picard-Vessiot extensions in terms of tensor products given by Levelt.
