Theorems · Definition · commutative algebra
ValuationSubring.primeSpectrumEquiv
{K : Type u} → [inst : Field K] → (A : ValuationSubring K) → PrimeSpectrum ↥A ≃ { S // A ≤ S }The equivalence between coarsenings of a valuation ring and its prime ideals.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivstatement · cited by 8,337
- Fieldstatement and proof · cited by 7,404
- PrimeSpectrumstatement and proof · cited by 625
- PrimeSpectrum.asIdealproof · cited by 333
- ValuationSubringstatement and proof · cited by 187
- ValuationSubring.ofPrimeproof · cited by 10
- ValuationSubring.idealOfLEproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- ValuationSubring.eq_self_or_eq_top_of_leproof · cited by 3
- ValuationSubring.primeSpectrumOrderEquivproof · cited by 2
- ValuationSubring.primeSpectrumEquiv_applystatement and proof · cited by 1