Theorems · Theorem · commutative algebra
MaximalSpectrum.mapPiLocalization.congr_simp
∀ {R : Type u_1} {S : Type u_2} [inst : CommSemiring R] [inst_1 : CommSemiring S] (f f_1 : R →+* S) (e_f : f = f_1)
(hf : Function.Bijective ⇑f), MaximalSpectrum.mapPiLocalization f hf = MaximalSpectrum.mapPiLocalization f_1 ⋯- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringCommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- RingHomstatement and proof · cited by 10,189
- Function.Bijectivestatement and proof · cited by 863
- Ideal.primeComplstatement · cited by 462
- Localization.AtPrimestatement · cited by 299
- MaximalSpectrumstatement · cited by 73
- MaximalSpectrum.asIdealstatement · cited by 58
- MaximalSpectrum.PiLocalizationstatement · cited by 17
- MaximalSpectrum.mapPiLocalizationstatement and proof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- MaximalSpectrum.mapPiLocalization_bijectiveproof · cited by 1