Theorems · Theorem · commutative algebra
PrimeSpectrum.mapPiLocalization_comp
∀ {R : Type u_1} {S : Type u_2} (P : Type u_3) [inst : CommSemiring R] [inst_1 : CommSemiring S]
[inst_2 : CommSemiring P] (f : R →+* S) (g : S →+* P),
PrimeSpectrum.mapPiLocalization (g.comp f) =
(PrimeSpectrum.mapPiLocalization g).comp (PrimeSpectrum.mapPiLocalization f)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
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.coeproof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement and proof · cited by 10,189
- RingHom.compstatement and proof · cited by 899
- PrimeSpectrumstatement and proof · cited by 625
- Ideal.primeComplstatement and proof · cited by 462
- Ideal.comapproof · cited by 443
- PrimeSpectrum.asIdealstatement and proof · cited by 333
- RingHom.extproof · cited by 331
- Localization.AtPrimeproof · cited by 299
- Localizationstatement and proof · cited by 270
- PrimeSpectrum.comapproof · cited by 199
Cited by1
Results whose statement or proof uses this declaration.
- PrimeSpectrum.mapPiLocalization_bijectiveproof · cited by 1