Theorems · Theorem · commutative algebra
Valuation.associated_of_isUniformizer
∀ {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 → v.IsUniformizer ↑π₂ → Associated π₁ π₂If two elements of K₀ are uniformizers, then they are associated.
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- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
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- Fieldstatement and proof · cited by 7,404
- one_mulproof · cited by 2,841
- Units.valproof · cited by 1,966
- map_mulproof · cited by 1,137
- Valuationstatement and proof · cited by 823
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- le_of_eqproof · cited by 366
- Associatedstatement · cited by 296
- inv_mul_cancel₀proof · cited by 267
- IsUnit.unitproof · cited by 252
- Subtype.val_injectiveproof · cited by 232
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