The Stacks project

Definition 10.162.9. Let $(R, \mathfrak m)$ be a Noetherian local ring. We say $R$ is analytically unramified if its completion $R^\wedge = \mathop{\mathrm{lim}}\nolimits _ n R/\mathfrak m^ n$ is reduced. A prime ideal $\mathfrak p \subset R$ is said to be analytically unramified if $R/\mathfrak p$ is analytically unramified.