Proposition 14

Let $A$ be a ring, $B$ a commutative $A$-algebra and $T$ a multiplicative subset of $B$. If $N$ is a $B$-module which is flat as an $A$-module, $T^{-1}N$ is a flat $A$-module.

$T^{-1}N = T^{-1}B \otimes_B N$; the proposition then follows from Chapter I, § 2, no. 7, Proposition 8, applied with $A$ replaced by $B$, $B$ by $A$, $E$ by $T^{-1}B$ and $F$ by $N$.