Lemma 10.82.10 (05CJ)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 10: Commutative Algebra
Section 10.82: Universally injective module maps
Lemma 10.82.10 (cite)

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Lemma 10.82.10. Let $R$ be a ring. Let $M \to M'$ and $M' \to M''$ be $R$ -module maps. If their composition $M \to M''$ is universally injective, then $M \to M'$ is universally injective.

Proof. Omitted. $\square$

Comments (1)

Comment #1402 by Fred Rohrer on April 13, 2015 at 20:59

Replace the second $M$ by $M'$ . After "If", insert "their composition".

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