\begin{definition}[Definition:Locally Noetherian Scheme]
Let $\struct {X, \OO_X}$ be a scheme.
Then $\struct {X, \OO_X}$ is '''locally noetherian''' {{iff}} every $x \in X$ is has an affine open neighborhood $U \subseteq X$ such that the ring $\map {\OO_X} U$ is noetherian.
Category:Definitions/Algebraic Geometry
Category:Definitions/Schemes
\end{definition}