Lemma 15.81.14. Let $R \to A \to B$ be finite type ring maps. Let $m \in \mathbf{Z}$. Let $M$ be an $A$-module. Assume $B$ is flat over $A$ and $B$ as a $B$-module is pseudo-coherent relative to $A$. If $M$ is $m$-pseudo-coherent (resp. pseudo-coherent) relative to $R$, then $M \otimes _ A B$ is $m$-pseudo-coherent (resp. pseudo-coherent) relative to $R$.

**Proof.**
Immediate from Lemma 15.81.13.
$\square$

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