Theorems · Theorem · algebraic geometry
PrimeSpectrum.toPiLocalizationEquiv_apply
∀ (R : Type u) [inst : CommSemiring R] [inst_1 : DiscreteTopology (PrimeSpectrum R)] (x : R), (PrimeSpectrum.toPiLocalizationEquiv R) x = (algebraMap R (PrimeSpectrum.PiLocalization R)) x
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- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringDiscreteTopology
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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
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement · cited by 4,706
- AlgEquivstatement · cited by 1,681
- 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.toPiLocalizationEquivstatement · cited by 3
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