Flatness is local
= Flatness is local
An $R$-module $M$ is flat if and only if $M_{\mathfrak p}$ is flat over $R_{\mathfrak p}$ for every <prime ideal> $\mathfrak p$, equivalently for every <maximal ideal>.
= Flatness is local
An $R$-module $M$ is flat if and only if $M_{\mathfrak p}$ is flat over $R_{\mathfrak p}$ for every <prime ideal> $\mathfrak p$, equivalently for every <maximal ideal>.