Noetherian scheme

In algebraic geometry, a noetherian scheme is a scheme that admits a finite covering by open affine subsets $\operatorname{Spec} A_i$ , $A_i$ noetherian rings. More generally, a scheme is locally noetherian if it is covered by spectra of noetherian rings. Thus, a scheme is noetherian if and only if it is locally noetherian and quasi-compact. As with noetherian rings, the concept is named after Emmy Noether.

单词	Noetherian scheme
释义	Noetherian scheme 英语百科 Noetherian scheme In algebraic geometry, a noetherian scheme is a scheme that admits a finite covering by open affine subsets $\operatorname{Spec} A_i$ , $A_i$ noetherian rings. More generally, a scheme is locally noetherian if it is covered by spectra of noetherian rings. Thus, a scheme is noetherian if and only if it is locally noetherian and quasi-compact. As with noetherian rings, the concept is named after Emmy Noether.
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