I was reading through Glaz's Commutative Coherent ring book, there I encountered a theorem where a part of it stated that
For two commutative rings with unity $S$ and $R$, where $S$ is a $R-$ algebra for a prime ideal $P \in Spec(S)$; $M_P$ is $R_P \cap_{R}$ flat, where $M$ is an $S$ module.
Now I am a bit confused in the notation, does the author want to imply that since $S$ is an $R$ algebra for every prime ideal $P\in Spec(S)$ if I take the contraction $p$ of $P$ in $R$ then $M_p$ is a flat $R_p$ module, or is it something else entirely.
Any insight or suggestion is most appreciated