Theorems · Theorem · algebraic geometry
AlgebraicGeometry.isNoetherian_Spec
∀ {R : CommRingCat}, AlgebraicGeometry.IsNoetherian (AlgebraicGeometry.Spec R) ↔ IsNoetherianRing ↑RR is a Noetherian ring if and only if Spec R is a Noetherian scheme.
- Defined in
- Mathlib.AlgebraicGeometry.Noetherian
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingCatstatement and proof · cited by 2,333
- CommRingCat.carrierstatement and proof · cited by 1,096
- AlgebraicGeometry.Specstatement and proof · cited by 626
- IsNoetherianRingstatement and proof · cited by 268
- AlgebraicGeometry.IsNoetherianstatement · cited by 10
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