Theorems · Theorem · commutative algebra
Ring.ordFrac_eq_valuation_inv
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDomain R] [inst_2 : IsDiscreteValuationRing R] {K : Type u_2}
[inst_3 : Field K] [inst_4 : Algebra R K] [inst_5 : IsFractionRing R K] (x : K),
(Ring.ordFrac R) x = ((IsDedekindDomain.HeightOneSpectrum.valuation K (IsDiscreteValuationRing.maximalIdeal R)) x)⁻¹- Cited by
- 4 results in Mathlib
- Foundations
- Depth 161 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.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- IsDomainstatement and proof · cited by 2,196
- Multiplicativestatement · cited by 875
- Valuationstatement · cited by 823
- IsFractionRingstatement and proof · cited by 738
- MonoidWithZeroHomstatement · cited by 704
- WithZerostatement · cited by 586
- IsDedekindDomain.HeightOneSpectrum.valuationstatement and proof · cited by 130
- IsDiscreteValuationRingstatement and proof · cited by 117
Cited by4
Results whose statement or proof uses this declaration.
- Ring.ordFrac_addproof · cited by 1
- Ring.isUnit_iff_ordFrac_one_of_isDiscreteValuationRingproof · cited by 0
- Ring.associated_of_ordFrac_eqproof · cited by 0
- Ring.ordFrac_irreducibleproof · cited by 0