Definition 3.3 ($I$-adic completion). Let $I\subseteq R$ be an ideal ($R$ a ring). The $I$-adic completion of $R$ is the

$$\widehat{R}:=\underset{\stackrel{[}{R}]\leftarrow }{\lim }∕I^n$$

where $R∕I^{n+1}\to R∕I^n$ is the natural projection.