Theorems · Theorem · commutative algebra
Valuation.IsUniformizer.is_generator
∀ {Γ : Type u_1} [inst : LinearOrderedCommGroupWithZero Γ] {K : Type u_2} [inst_1 : Field K] {v : Valuation K Γ}
[hv : v.IsRankOneDiscrete] {π : ↥v.valuationSubring},
v.IsUniformizer ↑π → IsLocalRing.maximalIdeal ↥v.valuationSubring = Ideal.span {π}- Cited by
- 0 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Fieldstatement and proof · cited by 7,404
- Idealstatement · cited by 4,748
- Ideal.spanstatement · cited by 948
- Valuationstatement and proof · cited by 823
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- IsLocalRing.maximalIdealstatement · cited by 297
- ValuationSubringstatement · cited by 187
- Valuation.valuationSubringstatement and proof · cited by 56
- Valuation.IsRankOneDiscretestatement and proof · cited by 53
- Valuation.IsUniformizerstatement and proof · cited by 22
- Valuation.Uniformizer.is_generatorproof · cited by 4
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