Theorems · Theorem · algebraic geometry
PrimeSpectrum.isJacobsonRing_iff_jacobsonSpace
∀ {R : Type u_1} [inst : CommRing R], IsJacobsonRing R ↔ JacobsonSpace (PrimeSpectrum R)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- SetLike.coeproof · cited by 8,199
- Idealproof · cited by 4,748
- le_antisymmproof · cited by 2,068
- PrimeSpectrumstatement and proof · cited by 625
- PrimeSpectrum.zeroLocusproof · cited by 164
- Ideal.radicalproof · cited by 121
- sInf_leproof · cited by 110
- Ideal.jacobsonproof · cited by 88
- IsClosed.closure_subset_iffproof · cited by 59
- IsJacobsonRingstatement and proof · cited by 40
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.LocallyOfFiniteType.jacobsonSpaceproof · cited by 2
- AlgebraicGeometry.isFinite_iff_locallyOfFiniteType_of_jacobsonSpaceproof · cited by 1