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— Let (X, 0) be a germ of an analytic coherent set in R'. Assume that analytic functions g^ ...,^p generate ideal I(X)oThere exists an increasing function e : N -»• N such that, for any function/of class C*^ vanishing on X, there exist C-f unctions q>i, ..., <pp such that /=<pi .gi +... +<Py.^p. In this paper we investigate the problem of the estimation of e (r) in some special cases. Let (X, 0) be a germ of an analytic coherent set in R'. Assume that analytic functions ^i, . .., gp generate the ideal

On the division of functions of class $C\sp r$ by real analytic functions