Corollary 6

Tag 049V, permanent. Cite it as [Bourbaki, Tag 049V].

Commutative Algebra, chapter II, § 4. Spectra of rings and supports of modules

The closure of a set consisting of a point $p \in X = \mathrm{Spec}(A)$ is the set $V(p)$ of prime ideals containing $p$ . For the set $\{p\}$ to be closed in $X$ (or, as we shall also say by an abuse of language, for $p$ to be a closedpoint of $X$ ), it is necessary and sufficient that $p$ be maximal.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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Cites

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