Lemma 10.41.4 (00HX)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 10: Commutative Algebra
Section 10.41: Going up and going down
Lemma 10.41.4 (cite)

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Lemma 10.41.4. Suppose $R \to S$ and $S \to T$ are ring maps satisfying going down. Then so does $R \to T$ . Similarly for going up.

Proof. According to Lemma 10.41.3 this follows from Topology, Lemma 5.19.5 $\square$

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