Lemma 10.138.4 (00TK)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 10: Commutative Algebra
Section 10.138: Formally smooth maps
Lemma 10.138.4 (cite)

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Lemma 10.138.4. A polynomial ring over $R$ is formally smooth over $R$ .

Proof. Suppose we have a diagram as in Definition 10.138.1 with $S = R[x_ j; j \in J]$ . Then there exists a dotted arrow simply by choosing lifts $a_ j \in A$ of the elements in $A/I$ to which the elements $x_ j$ map to under the top horizontal arrow. $\square$

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