Theorems · Theorem · algebraic geometry
PrimeSpectrum.toPiLocalization_bijective
∀ {R : Type u} [inst : CommSemiring R] [DiscreteTopology (PrimeSpectrum R)],
Function.Bijective ⇑(PrimeSpectrum.toPiLocalization R)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringDiscreteTopology
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- AlgHomstatement · cited by 3,236
- Function.Bijectivestatement · cited by 863
- PrimeSpectrumstatement and proof · cited by 625
- Ideal.primeComplstatement · cited by 462
- DiscreteTopologystatement and proof · cited by 373
- PrimeSpectrum.asIdealstatement · cited by 333
- Localizationstatement · cited by 270
- PrimeSpectrum.PiLocalizationstatement · cited by 20
- PrimeSpectrum.toPiLocalizationstatement · cited by 13
- PrimeSpectrum.discreteTopology_iff_toPiLocalization_bijectiveproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- PrimeSpectrum.toPiLocalizationEquivproof · cited by 3
- IsArtinianRing.exists_not_mem_forall_mem_of_neproof · cited by 1