The Stacks project

Lemma 10.13.6. Let $R$ be a ring and let $S \subset R$ be a multiplicative subset. Then $S^{-1}T_ R(M) = T_{S^{-1}R}(S^{-1}M)$ for any $R$-module $M$. Similar for symmetric and exterior algebras.

Proof. Omitted. Hint: Apply Lemma 10.12.16. $\square$

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