Theorems · Definition · commutative algebra
ValuationSubring.primeSpectrumOrderEquiv
{K : Type u} → [inst : Field K] → (A : ValuationSubring K) → (PrimeSpectrum ↥A)ᵒᵈ ≃o { S // A ≤ S }An ordered variant of primeSpectrumEquiv.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 90 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivproof · cited by 8,337
- Fieldstatement and proof · cited by 7,404
- OrderDualstatement and proof · cited by 927
- OrderIsostatement · cited by 874
- PrimeSpectrumstatement and proof · cited by 625
- OrderDual.ofDualproof · cited by 400
- Equiv.transproof · cited by 337
- ValuationSubringstatement and proof · cited by 187
- ValuationSubring.primeSpectrumEquivproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- ValuationSubring.primeSpectrumOrderEquiv_apply_coe_carrierstatement · cited by 0
- ValuationSubring.coe_primeSpectrumOrderEquiv_symm_apply_asIdealstatement and proof · cited by 0