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Let $R$ be a commutative ring and let $I$ be its nilradical. When is $R$ complete with respect to $I$?

For example, if $I$ is finitely generated, there exists $N$ such that $I^N = 0$ and thus $R$ is complete with respect to $I$.

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    $\begingroup$ For the same reason it's true if the nilradical is itself a nilpotent ideal. I doubt it's necessary, but one necessary condition is $\bigcap_n I^n=\{0\}$, so for instance taking something like the Puiseaux ring modulo $x$ will give a nonexample. I'm not sure exactly what kind of answer you expect. $\endgroup$
    – Wojowu
    Commented Jul 17 at 10:15

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