Theorems · Theorem · commutative algebra
Valuation.exists_pow_Uniformizer
∀ {Γ : Type u_1} [inst : LinearOrderedCommGroupWithZero Γ] {K : Type u_2} [inst_1 : Field K] {v : Valuation K Γ}
[hv : v.IsRankOneDiscrete] {r : ↥v.valuationSubring}, r ≠ 0 → ∀ (π : v.Uniformizer), ∃ n u, ↑r = ↑(π.val ^ n) * ↑↑u- Cited by
- 3 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites52
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- Set.rangeproof · cited by 4,705
- Subgroupproof · cited by 3,593
- one_mulproof · cited by 2,841
- Unitsstatement and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- mul_assocproof · cited by 1,667
- IsUnitproof · cited by 1,602
- map_mulproof · cited by 1,137
- Valuationstatement and proof · cited by 823
- Subringstatement · cited by 602
Cited by3
Results whose statement or proof uses this declaration.
- Valuation.Uniformizer.is_generatorproof · cited by 4
- Valuation.ideal_isPrincipalproof · cited by 1
- Valuation.isUniformizer_of_maximalIdeal_eq_spanproof · cited by 0