Definition 10.96.2. Let $R$ be a ring. Let $I \subset R$ be an ideal. Let $M$ be an $R$-module. We say $M$ is *$I$-adically complete* if the map

\[ M \longrightarrow M^\wedge = \mathop{\mathrm{lim}}\nolimits _ n M/I^ nM \]

is an isomorphism^{1}. We say $R$ is *$I$-adically complete* if $R$ is $I$-adically complete as an $R$-module.

## Comments (0)