Theorems · Theorem · number theory
NumberField.IsCMField.Units.complexConj_eq_self_iff
∀ (K : Type u_1) [inst : Field K] [inst_1 : CharZero K] [inst_2 : NumberField.IsCMField K]
[inst_3 : Algebra.IsIntegral ℚ K] (u : (NumberField.RingOfIntegers K)ˣ),
(NumberField.IsCMField.complexConj K) ((algebraMap (NumberField.RingOfIntegers K) K) ↑u) =
(algebraMap (NumberField.RingOfIntegers K) K) ↑u ↔
∃ v,
(algebraMap (NumberField.RingOfIntegers ↥(NumberField.maximalRealSubfield K)) K) ↑v =
(algebraMap (NumberField.RingOfIntegers K) K) ↑u- Defined in
- Mathlib.NumberTheory.NumberField.CMField
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 309 from the axioms · uses propext, Classical.choice, Quot.sound
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- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
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- Units.valstatement and proof · cited by 1,966
- AlgEquivstatement · cited by 1,681
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- CharZerostatement and proof · cited by 932
- NumberField.RingOfIntegersstatement and proof · cited by 413
- Subfieldstatement · cited by 303
- IsUnit.unitproof · cited by 252
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