Theorems · Theorem · commutative algebra
Valuation.isUniformizer_of_maximalIdeal_eq_span
∀ {Γ : Type u_1} [inst : LinearOrderedCommGroupWithZero Γ] {K : Type u_2} [inst_1 : Field K] (v : Valuation K Γ)
[inst_2 : v.IsRankOneDiscrete] {r : ↥v.valuationSubring},
IsLocalRing.maximalIdeal ↥v.valuationSubring = Ideal.span {r} → v.IsUniformizer ↑r- Cited by
- 0 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Fieldstatement and proof · cited by 7,404
- Idealstatement and proof · cited by 4,748
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- Ideal.spanstatement and proof · cited by 948
- Valuationstatement and proof · cited by 823
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- IsLocalRing.maximalIdealstatement and proof · cited by 297
- ValuationSubringstatement · cited by 187
- Valuation.valuationSubringstatement and proof · cited by 56
- Valuation.IsRankOneDiscretestatement and proof · cited by 53
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