  Let A be a polynomial algebra with complex coefficients. Let B be a finite
extension ring of A which is also a polynomial algebra. We describe the
factorisation of the Jacobian J of the extension into irreducibles. We also
introduce the notion of a well-ramified extension and define its discriminant
polynomial D. In the particular case where A is the ring of invariants of B
under the action of a group (i.e., a Galois extension), this framework
corresponds to the classical invariant theory of complex reflection groups. In
the more general case of a well-ramified extension, we explain how the pair
(D,J) behaves similarly to a Galois extension. This work can be viewed as the
first step towards a possible invariant theory of "virtual reflection groups".
