Theorems · Theorem · algebraic geometry
AlgebraicGeometry.isLocallyNoetherian_Spec
∀ {R : CommRingCat}, AlgebraicGeometry.IsLocallyNoetherian (AlgebraicGeometry.Spec R) ↔ IsNoetherianRing ↑R- Defined in
- Mathlib.AlgebraicGeometry.Noetherian
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functor.objproof · cited by 19,642
- Top.topproof · cited by 9,680
- CommRingCatstatement and proof · cited by 2,333
- AlgebraicGeometry.SheafedSpace.toPresheafedSpaceproof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpaceproof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpaceproof · cited by 1,734
- AlgebraicGeometry.PresheafedSpace.presheafproof · cited by 1,104
- CommRingCat.carrierstatement and proof · cited by 1,096
- AlgebraicGeometry.Specstatement and proof · cited by 626
- IsNoetherianRingstatement and proof · cited by 268
- AlgebraicGeometry.Scheme.ΓSpecIsoproof · cited by 106
- CategoryTheory.Iso.commRingCatIsoToRingEquivproof · cited by 44
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