Definition 10.150.1 (00UQ)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 10: Commutative Algebra
Section 10.150: Formally étale maps
Definition 10.150.1 (cite)

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Definition 10.150.1. Let $R \to S$ be a ring map. We say $S$ is formally étale over $R$ if for every commutative solid diagram

$\xymatrix{ S \ar[r] \ar@{-->}[rd] & A/I \\ R \ar[r] \ar[u] & A \ar[u] }$

where $I \subset A$ is an ideal of square zero, there exists a unique dotted arrow making the diagram commute.

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