Definition 10.65.1. Let $R$ be a ring. Let $M$ be an $R$-module. A prime $\mathfrak p$ of $R$ is *weakly associated* to $M$ if there exists an element $m \in M$ such that $\mathfrak p$ is minimal among the prime ideals containing the annihilator $\text{Ann}(m) = \{ f \in R \mid fm = 0\} $. The set of all such primes is denoted $\text{WeakAss}_ R(M)$ or $\text{WeakAss}(M)$.

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