The Stacks project

Definition 10.40.1. Let $R$ be a ring and let $M$ be an $R$-module. The support of $M$ is the set

\[ \text{Supp}(M) = \{ \mathfrak p \in \mathop{\mathrm{Spec}}(R) \mid M_{\mathfrak p} \not= 0 \} \]

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View Definition 10.40.1 as pdf