Locally Noetherian scheme
= Locally Noetherian scheme
A <scheme> is locally Noetherian if it has an <affine open cover> by spectra of <Noetherian rings>. It is a <Noetherian scheme> exactly when it is also a <quasi-compact scheme>: a finite subcover then supplies the required finite <affine open cover>. An infinite gluing of spectra of <Noetherian rings> along <open subschemes> is still locally Noetherian, but need not be a <quasi-compact scheme>.