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"Mouttaki, Hlal"
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A division's theorem on some class of \\(C^ınfty\\)-functions
Let \\(E_n\\) be the ring of the germs of \\(C^ınfty\\)-functions at the origin in \\(^n\\). It is well known that if \\(I\\) is an ideal of \\(E_n\\), generated by a finite number of germs of analytic functions, then \\(I\\) is closed. In this paper we consider an ideal of \\(E_n\\) generated by a finite number of germs in some class of \\(C^ınfty\\)-functions that are not analytic in \\(à\\), but quasi-analytic and we shall prove that the result holds in this general situation. We remark that the result is not true for a general ideal of finite type of \\(E_n\\).
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