The Stacks project

Definition 111.36.5. A scheme $X$ is called locally Noetherian if and only if for every point $x \in X$ there exists an affine open $\mathop{\mathrm{Spec}}(R) = U \subset X$ such that $R$ is Noetherian. A scheme is Noetherian if it is locally Noetherian and quasi-compact.

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