Lemma 15.61.4. Let $R \to A$ and $R \to B$ be ring maps. Let $R \to R'$ be a ring map and set $A' = A \otimes _ R R'$ and $B' = B \otimes _ R R'$. If $A$ and $B$ are tor independent over $R$ and $R \to R'$ is flat, then $A'$ and $B'$ are tor independent over $R'$.

Proof. Follows immediately from Lemma 15.61.3 and Definition 15.61.1. $\square$

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