Theorems · Definition · commutative algebra
ValuationSubring.unitGroup
{K : Type u} → [inst : Field K] → ValuationSubring K → Subgroup KˣThe unit group of a valuation subring, as a subgroup of Kˣ.
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 79 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.
- Fieldstatement and proof · cited by 7,404
- Subgroupstatement · cited by 3,593
- Unitsstatement · cited by 2,804
- MonoidHom.compproof · cited by 469
- MonoidHom.kerproof · cited by 212
- ValuationSubringstatement and proof · cited by 187
- Units.coeHomproof · cited by 44
- MonoidWithZeroHom.toMonoidHomproof · cited by 39
- ValuationSubring.valuationproof · cited by 29
- Valuation.toMonoidWithZeroHomproof · cited by 16
Cited by21
Results whose statement or proof uses this declaration.
- ValuationSubring.unitGroupMulEquivstatement and proof · cited by 7
- Set.unitproof · cited by 5
- ValuationSubring.unitGroupToResidueFieldUnitsstatement · cited by 5
- ValuationSubring.unitsModPrincipalUnitsEquivResidueFieldUnitsstatement and proof · cited by 2
- ValuationSubring.unitGroup_injectivestatement and proof · cited by 1
- ValuationSubring.unitGroupOrderEmbeddingproof · cited by 1
- ValuationSubring.ker_unitGroupToResidueFieldUnitsstatement and proof · cited by 0
- ValuationSubring.principal_units_le_unitsstatement · cited by 0
- Set.unit_eqstatement and proof · cited by 0
- ValuationSubring.coe_mem_principalUnitGroup_iffstatement and proof · cited by 0
- ValuationSubring.coe_unitGroupMulEquiv_applystatement and proof · cited by 0
- ValuationSubring.coe_unitGroupMulEquiv_symm_applystatement · cited by 0