Theorems · Theorem · commutative algebra
Valuation.IsUniformizer.of_associated
∀ {Γ : Type u_1} [inst : LinearOrderedCommGroupWithZero Γ] {K : Type u_2} [inst_1 : Field K] {v : Valuation K Γ}
[hv : v.IsRankOneDiscrete] {π₁ π₂ : ↥v.valuationSubring}, v.IsUniformizer ↑π₁ → Associated π₁ π₂ → v.IsUniformizer ↑π₂An element associated to a uniformizer is itself a uniformizer.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- mul_oneproof · cited by 3,885
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- map_mulproof · cited by 1,137
- Valuationstatement and proof · cited by 823
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- Associatedstatement and proof · cited by 296
- ValuationSubringstatement · cited by 187
- Units.isUnitproof · cited by 116
- Valuation.valuationSubringstatement and proof · cited by 56
Cited by1
Results whose statement or proof uses this declaration.
- Valuation.isUniformizer_of_maximalIdeal_eq_spanproof · cited by 0