Theorems · Theorem · commutative algebra
PrimeSpectrum.finite_of_toPiLocalization_surjective
∀ {R : Type u_1} [inst : CommSemiring R],
Function.Surjective ⇑(PrimeSpectrum.toPiLocalization R) → Finite (PrimeSpectrum R)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 83 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.
Cites21
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
- RingHomproof · cited by 10,189
- AlgHomstatement · cited by 3,236
- Finitestatement · cited by 3,029
- RingHomClass.toRingHomproof · cited by 746
- PrimeSpectrumstatement · cited by 625
- AlgHom.toRingHomproof · cited by 490
- Ideal.primeComplstatement · cited by 462
- PrimeSpectrum.asIdealstatement · cited by 333
- Localizationstatement · cited by 270
- Function.Surjective.of_compproof · cited by 30
Cited by1
Results whose statement or proof uses this declaration.
- PrimeSpectrum.discreteTopology_of_toLocalization_surjectiveproof · cited by 1