The Stacks project

Exercise 111.55.4. Let $A$ be a ring. Let $S \subset T \subset A$ be multiplicative subsets. Assume that

\[ \{ \mathfrak q \mid \mathfrak q \cap S = \emptyset \} = \{ \mathfrak q \mid \mathfrak q \cap T = \emptyset \} . \]

Show that $S^{-1}A \to T^{-1}A$ is an isomorphism.

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View Exercise 111.55.4 as pdf