Theorems · Definition · commutative algebra
Valuation.RankLeOne.rankOne_of_nontrivial
{Γ₀ : Type u_2} →
[inst : LinearOrderedCommGroupWithZero Γ₀] →
{K : Type u_3} →
[inst_1 : DivisionRing K] →
(v : Valuation K Γ₀) → [v.RankLeOne] → Nontrivial (MonoidWithZeroHom.ofClass v).ValueGroup₀ˣ → v.RankOneIf a valuation has rank at most one and is non trivial, then it has rank one
- Defined in
- Mathlib.RingTheory.Valuation.RankOne
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Subgroupstatement · cited by 3,593
- Unitsstatement and proof · cited by 2,804
- Nontrivialstatement and proof · cited by 2,416
- DivisionRingstatement and proof · cited by 1,062
- Valuationstatement and proof · cited by 823
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- MonoidWithZeroHom.ofClassstatement and proof · cited by 204
- MonoidWithZeroHom.valueGroupstatement · cited by 170
- MonoidWithZeroHom.ValueGroup₀statement and proof · cited by 166
- Valuation.RankOnestatement · cited by 32
- Valuation.RankLeOnestatement and proof · cited by 2
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