Theorems · Theorem · field theory

X_pow_mul_sub_C_irreducible

∀ {K : Type u} [inst : Field K] {n m : ℕ} {a : K},
  Irreducible (Polynomial.X ^ m - Polynomial.C a) →
    (∀ (E : Type u) [inst_1 : Field E] [inst_2 : Algebra K E] (x : E),
        minpoly K x = Polynomial.X ^ m - Polynomial.C a →
          Irreducible (Polynomial.X ^ n - Polynomial.C (IntermediateField.AdjoinSimple.gen K x))) →
      Irreducible (Polynomial.X ^ (n * m) - Polynomial.C a)

Defined in: Mathlib.FieldTheory.KummerExtension
Cited by: 1 results in Mathlib
Foundations: Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field

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X_pow_sub_C_irreducible_of_oddproof · cited by 3