Definition:Locally Noetherian Scheme

Definition

Let $\struct {X, \OO_X}$ be a scheme.

Then $\struct {X, \OO_X}$ is locally noetherian if and only if every $x \in X$ is has an affine open neighborhood $U \subseteq X$ such that the ring $\map {\OO_X} U$ is noetherian.

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