Theorems · Theorem · commutative algebra
Ring.ordFrac_eq_inverse_comp_valuation
∀ {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],
Ring.ordFrac R =
MonoidWithZero.inverse.comp
(IsDedekindDomain.HeightOneSpectrum.valuation K (IsDiscreteValuationRing.maximalIdeal R)).toMonoidWithZeroHom- Cited by
- 2 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites32
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · 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
- Algebra.algebraMapproof · cited by 4,706
- IsDomainstatement and proof · cited by 2,196
- map_zeroproof · cited by 1,614
- nonZeroDivisorsproof · cited by 895
- Multiplicativestatement · cited by 875
- IsFractionRingstatement and proof · cited by 738
- MonoidWithZeroHomstatement · cited by 704
- WithZerostatement · cited by 586
Cited by2
Results whose statement or proof uses this declaration.
- Ring.ordFrac_eq_valuation_invproof · cited by 4
- Ring.mker_ordFrac_eq_isUnitSubmonoidproof · cited by 0