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
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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