Lemma 10.66.14 (05C8)—The Stacks project

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Part 1: Preliminaries
Chapter 10: Commutative Algebra
Section 10.66: Weakly associated primes
Lemma 10.66.14 (cite)

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Lemma 10.66.14. Let $R$ be a ring. Let $I$ be an ideal. Let $M$ be an $R/I$-module. Via the canonical injection $\mathop{\mathrm{Spec}}(R/I) \to \mathop{\mathrm{Spec}}(R)$ we have $\text{WeakAss}_{R/I}(M) = \text{WeakAss}_ R(M)$.

Proof. Special case of Lemma 10.66.13. $\square$

Comments (2)

Comment #3772 by Laurent Moret-Bailly on November 04, 2018 at 14:08

"Follows from Lemma 05E1" is better than "Omitted"!

Comment #3902 by Johan on January 22, 2019 at 10:50

Indeed! Thanks and fixed here.

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