Lemma 10.138.9. Let $A \to B \to C$ be ring maps. Assume $B \to C$ is formally smooth. Then the sequence

\[ 0 \to \Omega _{B/A} \otimes _ B C \to \Omega _{C/A} \to \Omega _{C/B} \to 0 \]

of Lemma 10.131.7 is a split short exact sequence.

Lemma 10.138.9. Let $A \to B \to C$ be ring maps. Assume $B \to C$ is formally smooth. Then the sequence

\[ 0 \to \Omega _{B/A} \otimes _ B C \to \Omega _{C/A} \to \Omega _{C/B} \to 0 \]

of Lemma 10.131.7 is a split short exact sequence.

**Proof.**
Follows from Proposition 10.138.8 and Lemma 10.134.4.
$\square$

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