Theorems · Definition · number theory
RatFunc.valuationIdeal
{K : Type u_1} →
{Γ : Type u_2} →
[inst : Field K] →
[inst_1 : LinearOrderedCommGroupWithZero Γ] →
{v : Valuation (RatFunc K) Γ} →
[v.IsNontrivial] →
[Valuation.IsTrivialOn K v] → v RatFunc.X ≤ 1 → IsDedekindDomain.HeightOneSpectrum (Polynomial K)The maximal ideal of K[X] generated by the uniformizingPolynomial for v.
- Defined in
- Mathlib.NumberTheory.RatFunc.Ostrowski
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Submodule.spanproof · cited by 1,504
- Valuationstatement and proof · cited by 823
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- IsDedekindDomain.HeightOneSpectrumstatement · cited by 338
- RatFuncstatement and proof · cited by 301
- RatFunc.Xstatement and proof · cited by 58
- Valuation.IsTrivialOnstatement and proof · cited by 28
- Valuation.IsNontrivialstatement and proof · cited by 27
- RatFunc.uniformizingPolynomialproof · cited by 7
Cited by5
Results whose statement or proof uses this declaration.
- RatFunc.valuation_eq_valuation_uniformizingPolynomial_pow_of_valuation_X_le_onestatement and proof · cited by 2
- RatFunc.exists_zpow_uniformizingPolynomialproof · cited by 1
- RatFunc.valuation_isEquiv_adic_of_valuation_X_le_oneproof · cited by 1
- RatFunc.valuation_isEquiv_valuationIdeal_adic_of_valuation_X_le_onestatement and proof · cited by 1
- RatFunc.valuationIdeal.congr_simpstatement and proof · cited by 0