Theorems · Theorem · commutative algebra
Valuation.nonempty_rankOne_iff_mulArchimedean
∀ {R : Type u_1} {Γ₀ : Type u_2} [inst : Ring R] [inst_1 : LinearOrderedCommGroupWithZero Γ₀] {v : Valuation R Γ₀}
[v.IsNontrivial], Nonempty v.RankOne ↔ MulArchimedean (MonoidWithZeroHom.ofClass v).ValueGroup₀- Defined in
- Mathlib.RingTheory.Valuation.RankOne
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites50
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realproof · cited by 25,697
- Ringstatement and proof · cited by 7,463
- NNRealproof · cited by 4,310
- MonoidHomproof · cited by 3,629
- Subgroupstatement · cited by 3,593
- Unitsstatement and proof · cited by 2,804
- Units.valproof · cited by 1,966
- NNReal.toRealproof · cited by 1,260
- le_of_ltproof · cited by 1,175
- Multiplicativeproof · cited by 875
- Valuationstatement and proof · cited by 823
Cited by1
Results whose statement or proof uses this declaration.
- ValuativeRel.isRankLeOne_iff_mulArchimedeanproof · cited by 1