Theorems · Definition · commutative algebra
Valuation.valuationSubring
{K : Type u} →
[inst : Field K] → {Γ : Type u_1} → [inst_1 : LinearOrderedCommGroupWithZero Γ] → Valuation K Γ → ValuationSubring KThe valuation subring associated to a valuation.
- Cited by
- 56 results in Mathlib
- Foundations
- Depth 50 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Valuationstatement and proof · cited by 823
- Subringproof · cited by 602
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- ValuationSubringstatement · cited by 187
- Valuation.integerproof · cited by 68
Cited by64
Results whose statement or proof uses this declaration.
- ArchimedeanClass.FiniteElementproof · cited by 36
- IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegersproof · cited by 22
- Set.integerproof · cited by 8
- Set.unitproof · cited by 5
- Rat.HeightOneSpectrum.adicCompletionIntegers.padicIntEquivproof · cited by 4
- Valuation.Uniformizer.is_generatorstatement and proof · cited by 4
- ArchimedeanClass.FiniteResidueField.mk_eq_zerostatement · cited by 3
- Valuation.exists_pow_Uniformizerstatement and proof · cited by 3
- ArchimedeanClass.FiniteElement.extstatement · cited by 2
- ArchimedeanClass.FiniteElement.not_isUnit_iff_mk_posstatement · cited by 2
- ArchimedeanClass.FiniteResidueField.mk_ne_zerostatement · cited by 2
- Valuation.exists_isUniformizer_of_isCyclic_of_nontrivialstatement and proof · cited by 2