Theorems · Theorem · field theory

autEquivZmod_symm_apply_intCast

∀ {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 : ℤ),
      ((autEquivZmod H L hζ).symm (Multiplicative.ofAdd ↑m)) α = ζ ^ m • α

Defined in: Mathlib.FieldTheory.KummerExtension
Cited by: 1 results in Mathlib
Foundations: Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Algebra Polynomial.IsSplittingField NeZero

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Algebrastatement and proof · cited by 11,388
RingHomstatement · cited by 10,189
Equivstatement · cited by 8,337
Fieldstatement and proof · cited by 7,404
Polynomialstatement · cited by 5,681
Algebra.algebraMapstatement and proof · cited by 4,706
AlgEquivstatement · cited by 1,681
Polynomial.Xstatement and proof · cited by 1,639
Polynomial.Cstatement and proof · cited by 1,598
MulEquivstatement · cited by 1,142
ZModstatement · cited by 1,024

Cited by1

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autEquivZmod_symm_apply_natCastproof · cited by 0