Theorems · Definition · commutative algebra
MaximalSpectrum.PiLocalization
(R : Type u_1) → [CommSemiring R] → Type u_1
The product of localizations at all maximal ideals of a commutative semiring.
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 71 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.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Localization.AtPrimeproof · cited by 299
- MaximalSpectrumproof · cited by 73
- MaximalSpectrum.asIdealproof · cited by 58
Cited by22
Results whose statement or proof uses this declaration.
- MaximalSpectrum.toPiLocalizationstatement and proof · cited by 9
- MaximalSpectrum.mapPiLocalizationstatement · cited by 6
- PrimeSpectrum.piLocalizationToMaximalstatement · cited by 3
- MaximalSpectrum.toPiLocalization_injectivestatement · cited by 3
- PrimeSpectrum.piLocalizationToMaximal_comp_toPiLocalizationstatement · cited by 2
- PrimeSpectrum.piLocalizationToMaximal_surjectivestatement and proof · cited by 2
- MaximalSpectrum.toPiLocalizationEquivstatement · cited by 2
- MaximalSpectrum.toPiLocalization_not_surjective_of_infinitestatement and proof · cited by 2
- PrimeSpectrum.piLocalizationToMaximalEquivstatement and proof · cited by 1
- MaximalSpectrum.mapPiLocalization.congr_simpstatement · cited by 1
- MaximalSpectrum.finite_of_toPiLocalization_pi_surjectivestatement · cited by 1
- MaximalSpectrum.mapPiLocalization_bijectivestatement and proof · cited by 1