Theorems · Theorem · commutative algebra
MaximalSpectrum.toPiLocalization_injective
∀ (R : Type u_1) [inst : CommSemiring R], Function.Injective ⇑(MaximalSpectrum.toPiLocalization R)
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 75 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.
Cites16
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
- Idealproof · cited by 4,748
- AlgHomstatement · cited by 3,236
- one_mulproof · cited by 2,841
- Ideal.primeComplstatement and proof · cited by 462
- Ideal.IsMaximalproof · cited by 452
- Localization.AtPrimestatement and proof · cited by 299
- MaximalSpectrumstatement · cited by 73
- MaximalSpectrum.asIdealstatement and proof · cited by 58
- Ideal.exists_le_maximalproof · cited by 47
- IsLocalization.eq_iff_existsproof · cited by 30
Cited by3
Results whose statement or proof uses this declaration.
- PrimeSpectrum.toPiLocalization_injectiveproof · cited by 2
- MaximalSpectrum.toPiLocalization_not_surjective_of_infiniteproof · cited by 2
- MaximalSpectrum.finite_of_toPiLocalization_surjectiveproof · cited by 0