Theorems · Theorem · commutative algebra
ValuationSubring.mem_principalUnitGroup_iff
∀ {K : Type u} [inst : Field K] (A : ValuationSubring K) (x : Kˣ), x ∈ A.principalUnitGroup ↔ A.valuation (↑x - 1) < 1- Cited by
- 1 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- Subgroupstatement · cited by 3,593
- Unitsstatement and proof · cited by 2,804
- Units.valstatement · cited by 1,966
- Valuationstatement · cited by 823
- ValuationSubringstatement and proof · cited by 187
- ValuationSubring.valuationstatement · cited by 29
- ValuationSubring.ValueGroupstatement · cited by 26
- ValuationSubring.principalUnitGroupstatement · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- ValuationSubring.principalUnitGroup_le_principalUnitGroupproof · cited by 0