Geodesic
Rigid and Finitely V-Determined Germs of C∞-Mappings
Canadian journal of mathematics, Tome 25 (1973) no. 4, pp. 727-732

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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 determinants where Let Clearly, is an ideal in and where is the (unique) maximal ideal of . 
Bochnak, Jacek; Kuo, Tzee-Char. Rigid and Finitely V-Determined Germs of C∞-Mappings. Canadian journal of mathematics, Tome 25 (1973) no. 4, pp. 727-732. doi: 10.4153/CJM-1973-074-x
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