Theorems · Theorem · commutative algebra
PrimeSpectrum.toPiLocalization_injective
∀ (R : Type u_1) [inst : CommSemiring R], Function.Injective ⇑(PrimeSpectrum.toPiLocalization R)
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 76 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- AlgHomstatement · cited by 3,236
- PrimeSpectrumstatement · cited by 625
- Ideal.primeComplstatement · cited by 462
- PrimeSpectrum.asIdealstatement · cited by 333
- Localizationstatement · cited by 270
- MaximalSpectrumproof · cited by 73
- PrimeSpectrum.PiLocalizationstatement · cited by 20
- PrimeSpectrum.toPiLocalizationstatement and proof · cited by 13
- MaximalSpectrum.toPrimeSpectrumproof · cited by 5
- MaximalSpectrum.toPiLocalization_injectiveproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- PrimeSpectrum.discreteTopology_iff_toPiLocalization_bijectiveproof · cited by 2
- PrimeSpectrum.finite_of_toPiLocalization_surjectiveproof · cited by 1