Theorems · Theorem · commutative algebra
Valuation.IsUniformizer.val
∀ {Γ : Type u_1} [inst : LinearOrderedCommGroupWithZero Γ] {A : Type u_2} [inst_1 : Ring A] {v : Valuation A Γ}
[hv : v.IsRankOneDiscrete] {π : A}, v.IsUniformizer π → v π = ↑(Valuation.IsRankOneDiscrete.generator v)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Ringstatement and proof · cited by 7,463
- Units.valstatement · cited by 1,966
- Valuationstatement and proof · cited by 823
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- Valuation.IsRankOneDiscretestatement and proof · cited by 53
- Valuation.IsRankOneDiscrete.generatorstatement · cited by 24
- Valuation.IsUniformizerstatement and proof · cited by 22
Cited by3
Results whose statement or proof uses this declaration.
- RatFunc.valuation_isEquiv_valuationIdeal_adic_of_valuation_X_le_oneproof · cited by 1
- Valuation.IsUniformizer.zpowers_eq_valueGroupproof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.intValuation_uniformizerproof · cited by 0