Theorems · Theorem · number theory

NumberField.IsCMField.ringOfIntegersComplexConj_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] (x : NumberField.RingOfIntegers K),
  (NumberField.IsCMField.ringOfIntegersComplexConj K) x = x ↔
    x ∈
      Set.range
        ⇑(algebraMap (NumberField.RingOfIntegers ↥(NumberField.maximalRealSubfield K)) (NumberField.RingOfIntegers K))

Defined in: Mathlib.NumberTheory.NumberField.CMField
Cited by: 0 results in Mathlib
Foundations: Depth 309 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field CharZero NumberField.IsCMField Algebra.IsIntegral

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DFunLike.coestatement and proof · cited by 62,936
Setstatement · cited by 53,352
RingHomstatement · cited by 10,189
Fieldstatement and proof · cited by 7,404
Algebra.algebraMapstatement and proof · cited by 4,706
Set.rangestatement and proof · cited by 4,705
AlgEquivstatement · cited by 1,681
CharZerostatement and proof · cited by 932
NumberField.RingOfIntegersstatement and proof · cited by 413
Subfieldstatement · cited by 303
Algebra.IsIntegralstatement and proof · cited by 224
NumberField.RingOfIntegers.valproof · cited by 74

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