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The Stacks project

Lemma 38.14.4. Let R be a henselian local ring with maximal ideal \mathfrak m. Let R \to S be a ring map. Let N be an S-module. Assume N is countably generated and Mittag-Leffler as an R-module. Then for any R-module M and for any prime \mathfrak q \subset S which is an associated prime of N \otimes _ R M we have \mathfrak q + \mathfrak m S \not= S.

Proof. This lemma reduces to Lemma 38.14.3 by Algebra, Lemma 10.153.13. \square

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