一般滤过和$C^r$方程的Artin-Tougeron型逼近结果
Approximation results of Artin-Tougeron-type for general filtrations and for $C^r$-equations
摘要：
Artin近似和其他相关的近似结果在各个领域都有应用。传统的制定这样的结果是有限的理想，$\{I^j\}$，和诺特环的权力过滤。本文将几个逼近结果推广到相当一般的滤子和$C^r$ -环上，得到了关于$2\le r\le\infty$的逼近结果.作为一个辅助步骤，我们建立满射的完成映射环的$C^\infty$功能，一个非常广泛的一类过滤。
英文摘要：
Artin approximation and other related approximation results are used in various areas. The traditional formulation of such results is restricted to filtrations by powers of ideals, $\{I^j\}$, and to Noetherian rings. In this paper we extend several approximation results both to rather general filtrations and to $C^r$-rings, for $2\le r\le\infty$. As an auxiliary step we establish the surjectivity of the completion map for rings of $C^\infty$ functions, for a very broad class of filtrations.
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