Theorems · Theorem · algebraic geometry
PrimeSpectrum.topologicalKrullDim_eq_ringKrullDim
∀ (R : Type u) [inst : CommSemiring R], topologicalKrullDim (PrimeSpectrum R) = ringKrullDim R
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- ENatstatement · cited by 4,985
- WithBotstatement · cited by 1,498
- PrimeSpectrumstatement · cited by 625
- OrderIso.symmproof · cited by 475
- ringKrullDimstatement · cited by 75
- Order.krullDim_eq_of_orderIsoproof · cited by 9
- Order.krullDim_orderDualproof · cited by 7
- topologicalKrullDimstatement · cited by 6
- PrimeSpectrum.pointsEquivIrreducibleClosedsproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsLocallyArtinian.of_topologicalKrullDim_le_zeroproof · cited by 2