Lemma 38.23.2. Let A be a ring. Let u : M \to N be a surjective map of A-modules. If M is projective as an A-module, then there exists an ideal I \subset A such that for any ring map \varphi : A \to B the following are equivalent
u \otimes 1 : M \otimes _ A B \to N \otimes _ A B is an isomorphism, and
\varphi (I) = 0.
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