Lemma 10.82.8 (05CH)—The Stacks project

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Part 1: Preliminaries
Chapter 10: Commutative Algebra
Section 10.82: Universally injective module maps
Lemma 10.82.8 (cite)

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Lemma 10.82.8. Let $R$ be a ring. Let $M \to M'$ be a universally injective $R$ -module map. Then for any $R$ -module $N$ the map $M \otimes _ R N \to M' \otimes _ R N$ is universally injective.

Proof. Omitted. $\square$

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