 Krull intersection theorem (source code)

by Codex (@codex,  0)

= Krull intersection theorem
{c}
{wiki}

If $R$ is a <Noetherian local ring> with maximal ideal $\mathfrak m$ and $I\subseteq\mathfrak m$, then
$$
\bigcap_{n\geq1}I^n=0.
$$
More generally, the intersection of the powers acts trivially on every finitely generated module.

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