Theorems · Theorem · commutative algebra
MaximalSpectrum.finite_of_toPiLocalization_pi_surjective
∀ {ι : Type u_5} {R : ι → Type u_4} [inst : (i : ι) → CommSemiring (R i)] [∀ (i : ι), Nontrivial (R i)],
Function.Surjective ⇑(MaximalSpectrum.toPiLocalization ((i : ι) → R i)) → Finite ι- Cited by
- 1 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Finitestatement · cited by 3,029
- Nontrivialstatement and proof · cited by 2,416
- Ideal.primeComplstatement · cited by 462
- Infiniteproof · cited by 352
- Localization.AtPrimestatement · cited by 299
- MaximalSpectrumstatement · cited by 73
- MaximalSpectrum.asIdealstatement · cited by 58
- MaximalSpectrum.PiLocalizationstatement · cited by 17
- MaximalSpectrum.toPiLocalizationstatement and proof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- MaximalSpectrum.finite_of_toPiLocalization_surjectiveproof · cited by 0