Theorems · Theorem · commutative algebra
Valuation.valuationSubring_not_isField
∀ {Γ : Type u_1} [inst : LinearOrderedCommGroupWithZero Γ] {K : Type u_2} [inst_1 : Field K] (v : Valuation K Γ)
[Nontrivial ↥(MonoidWithZeroHom.ofClass v).valueGroup] [IsCyclic ↥(MonoidWithZeroHom.ofClass v).valueGroup],
¬IsField ↥v.valuationSubring- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Subgroupstatement · cited by 3,593
- Unitsstatement and proof · cited by 2,804
- Nontrivialstatement and proof · cited by 2,416
- Valuationstatement and proof · cited by 823
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- MonoidWithZeroHom.ofClassstatement and proof · cited by 204
- ValuationSubringstatement · cited by 187
- MonoidWithZeroHom.valueGroupstatement and proof · cited by 170
- IsCyclicstatement and proof · cited by 122
- IsFieldstatement and proof · cited by 103
- Valuation.valuationSubringstatement and proof · cited by 56
Cited by1
Results whose statement or proof uses this declaration.
- Valuation.isUniformizer_of_maximalIdeal_eq_spanproof · cited by 0