Definition 10.63.1 (00LA)—The Stacks project

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Definition 10.63.1. Let $R$ be a ring. Let $M$ be an $R$ -module. A prime $\mathfrak p$ of $R$ is associated to $M$ if there exists an element $m \in M$ whose annihilator is $\mathfrak p$ . The set of all such primes is denoted $\text{Ass}_ R(M)$ or $\text{Ass}(M)$ .

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Comment #10002 by Shubhankar on February 22, 2025 at 07:45

Apologies for nitpicking, but should $m\neq 0$ ? Otherwise every prime is an associated prime.

Note that the definition of annihilator on the stacksproject allows annihilators of 0.

Comment #10003 by Shubhankar on February 22, 2025 at 08:13

sorry ignore, its obviously stupid

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