Non-existence of the Artin function for Henselian pairs.(English)Zbl 0803.13005

If $$(A,m)$$ is a local Henselian ring, the strong version of the Artin approximation theorem says that given a system of algebraic equations over $$A$$, a sufficiently good approximate solution in the $$m$$-adic topology can be approximated by an exact solution. The Artin function is a quantitative measure of “sufficiently good” in the above statement. The main point of this paper is to give a simple counterexample to the analogue of the above statement for Henselian pairs $$(A,I)$$.

MSC:

 13B40 Étale and flat extensions; Henselization; Artin approximation 13J15 Henselian rings
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References:

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