Theorems · Theorem · field theory

autEquivZmod_symm_apply_natCast

∀ {K : Type u} [inst : Field K] {n : ℕ} {a : K} (H : Irreducible (Polynomial.X ^ n - Polynomial.C a)) (L : Type u_1)
  [inst_1 : Field L] [inst_2 : Algebra K L]
  [inst_3 : Polynomial.IsSplittingField K L (Polynomial.X ^ n - Polynomial.C a)] {α : L},
  α ^ n = (algebraMap K L) a →
    ∀ [inst_4 : NeZero n] {ζ : K} (hζ : IsPrimitiveRoot ζ n) (m : ℕ),
      ((autEquivZmod H L hζ).symm (Multiplicative.ofAdd ↑m)) α = ζ ^ m • α

Defined in: Mathlib.FieldTheory.KummerExtension
Cited by: 0 results in Mathlib
Foundations: Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Algebra Polynomial.IsSplittingField NeZero

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Polynomial.Cstatement and proof · cited by 1,598
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ZModstatement · cited by 1,024

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