Theorems · Definition · number theory
NumberField.IsCMField.realUnits
(K : Type u_1) → [inst : Field K] → Subgroup (NumberField.RingOfIntegers K)ˣ
The subgroup of (𝓞 K)ˣ generated by the units of K⁺. These units are exactly the units fixed
by the complex conjugation, see IsCMField.unitsComplexConj_eq_self_iff.
- Defined in
- Mathlib.NumberTheory.NumberField.CMField
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 165 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.
Cites9
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
- Algebra.algebraMapproof · cited by 4,706
- Subgroupstatement · cited by 3,593
- Unitsstatement · cited by 2,804
- NumberField.RingOfIntegersstatement and proof · cited by 413
- MonoidHom.rangeproof · cited by 314
- RingHom.toMonoidHomproof · cited by 132
- Units.mapproof · cited by 95
- NumberField.maximalRealSubfieldproof · cited by 38
Cited by6
Results whose statement or proof uses this declaration.
- NumberField.IsCMField.indexRealUnitsproof · cited by 4
- NumberField.IsCMField.indexRealUnits_mul_eqproof · cited by 2
- NumberField.IsCMField.unitsComplexConj_eq_self_iffstatement and proof · cited by 1
- NumberField.IsCMField.unitsMulComplexConjInv_kerstatement and proof · cited by 1
- NumberField.IsCMField.closure_realFundSystem_sup_torsionstatement · cited by 1
- NumberField.IsCMField.mem_realUnits_iffstatement · cited by 0