A locally Noetherian scheme is a scheme that has an open cover by affine schemes 
with every 
a Noetherian ring. Equivalently,
every point has a Noetherian affine open neighborhood. A locally Noetherian scheme
is Noetherian when it is also quasi-compact.
Locally Noetherian Scheme
See also
Affine Scheme, Noetherian Ring, Regular Scheme, SchemeExplore with Wolfram|Alpha
References
Hartshorne, R. Algebraic Geometry. New York: Springer-Verlag, 1977.Cite this as:
Weisstein, Eric W. "Locally Noetherian Scheme." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LocallyNoetherianScheme.html