  We present a generalization of the Jacobian Conjecture for m polynomials in n
variables: f1,...,fm belonging to k[x1,...,xn], where k is a field of
characteristic zero and m=1,...,n. We express the generalized Jacobian
condition in terms of irreducible and square-free elements of the subalgebra
k[f1,...,fm]. We also discuss obtained properties in a more general setting -
for subrings of unique factorization domains.
