Theorems · Theorem · commutative algebra
IsDiscreteValuationRing.associated_of_valuation_eq
∀ {A : Type u_1} {K : Type u_2} [inst : CommRing A] [inst_1 : IsDomain A] [inst_2 : IsDiscreteValuationRing A]
[inst_3 : Field K] [inst_4 : Algebra A K] [inst_5 : IsFractionRing A K] (x y : K),
(IsDedekindDomain.HeightOneSpectrum.valuation K (IsDiscreteValuationRing.maximalIdeal A)) x =
(IsDedekindDomain.HeightOneSpectrum.valuation K (IsDiscreteValuationRing.maximalIdeal A)) y →
∃ u, u • x = y- Cited by
- 1 results in Mathlib
- Foundations
- Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
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
- SetLike.coeproof · cited by 8,199
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapproof · cited by 4,706
- mul_oneproof · cited by 3,885
- Submonoidproof · cited by 3,086
- one_mulproof · cited by 2,841
- Unitsstatement and proof · cited by 2,804
- IsDomainstatement and proof · cited by 2,196
- map_zeroproof · cited by 1,614
Cited by1
Results whose statement or proof uses this declaration.
- Ring.associated_of_ordFrac_eqproof · cited by 0