Rigid and Finitely V-Determined Germs of C∞-Mappings

Abstract

Let (respectively ) denote the ring of germs at 0 ∈ Rn of all C∞ functions (respectively Cμ functions) from Rn to R. For a given where is the space of all germs of C∞ mappings Rn → Rp, let J(φ) denote the ideal in generated by φ1, … , φp and the Jacobian determinantswhere LetClearly, is an ideal in and where is the (unique) maximal ideal of .