= Coefficient ideals of a formal power series ideal
{title2=$A_n=\{[X^n]f:f\in H\cap X^nR[[X]]\}$}
For an <ideal> $H\subseteq R[[X]]$, let $A_n$ consist of coefficients of $X^n$ in members of $H$ with all lower coefficients zero. These are <ideals> of $R$ and $A_n\subseteq A_{n+1}$, by multiplication by $X$. If $R$ is <Noetherian>, this chain stabilizes. Choose series whose leading coefficients generate the finitely many distinct coefficient <ideals>, then cancel coefficients successively. The accumulated multipliers are <formal power series>, giving an ordinary finite <ideal> generating set for $H$, rather than merely a dense subideal.
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