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 \((A,I)\).


13B40 √Čtale and flat extensions; Henselization; Artin approximation
13J15 Henselian rings
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