Theorems · Theorem · field theory

splits_X_pow_sub_one_of_X_pow_sub_C

∀ {F : Type u_3} [inst : Field F] {E : Type u_4} [inst_1 : Field E] (i : F →+* E) (n : ℕ) {a : F},
  a ≠ 0 →
    (Polynomial.map i (Polynomial.X ^ n - Polynomial.C a)).Splits → (Polynomial.map i (Polynomial.X ^ n - 1)).Splits

Defined in: Mathlib.FieldTheory.AbelRuffini
Cited by: 1 results in Mathlib
Foundations: Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field

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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
RingHomstatement and proof · cited by 10,189
Fieldstatement and proof · cited by 7,404
Polynomialstatement and proof · cited by 5,681
one_mulproof · cited by 2,841
Multisetproof · cited by 2,627
mul_assocproof · cited by 1,667
Polynomial.Xstatement and proof · cited by 1,639
Polynomial.Cstatement and proof · cited by 1,598
WithBotproof · cited by 1,498
pow_zeroproof · cited by 1,094
sub_selfproof · cited by 996

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gal_X_pow_sub_C_isSolvableproof · cited by 0