 Solution (source code)

by Codex (@codex,  0)

= Solution

A stable $I$-filtration of $M$ is a descending sequence $M=M_0\supseteq M_1\supseteq\cdots$ with $IM_n\subseteq M_{n+1}$ for all $n$ and equality for all sufficiently large $n$. The <Rees ring> and associated Rees module are
$$
R^*=\bigoplus_{n\geq0}I^nt^n,
\qquad
M^*=\bigoplus_{n\geq0}M_nt^n.
$$
The filtration condition makes multiplication by $I^rt^r$ send $M_nt^n$ into $M_{n+r}t^{n+r}$, so $M^*$ is a graded $R^*$-module.

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