Lemma 15.63.13. Let $A \to B$ be a flat ring map. Let $M$ be an $m$-pseudo-coherent (resp. pseudo-coherent) $A$-module. Then $M \otimes _ A B$ is an $m$-pseudo-coherent (resp. pseudo-coherent) $B$-module.

**Proof.**
Immediate consequence of Lemma 15.63.12 and the fact that $M \otimes _ A^{\mathbf{L}} B = M \otimes _ A B$ because $B$ is flat over $A$.
$\square$

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