Definition 31.4.1. Let $X$ be a scheme. Let $\mathcal{F}$ be a quasi-coherent sheaf on $X$.

1. An embedded associated point of $\mathcal{F}$ is an associated point which is not maximal among the associated points of $\mathcal{F}$, i.e., it is the specialization of another associated point of $\mathcal{F}$.

2. A point $x$ of $X$ is called an embedded point if $x$ is an embedded associated point of $\mathcal{O}_ X$.

3. An embedded component of $X$ is an irreducible closed subset $Z = \overline{\{ x\} }$ where $x$ is an embedded point of $X$.

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