Theorem 41.9.2. Let $A$, $B$ be Noetherian local rings. Let $f : A \to B$ be a local homomorphism. If $M$ is a finite $B$-module that is flat as an $A$-module, and $t \in \mathfrak m_ B$ is an element such that multiplication by $t$ is injective on $M/\mathfrak m_ AM$, then $M/tM$ is also $A$-flat.
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