Theorems · Theorem · field theory

isCyclic_of_isSplittingField_X_pow_sub_C

∀ {K : Type u} [inst : Field K] {n : ℕ},
  (primitiveRoots n K).Nonempty →
    ∀ {a : K},
      Irreducible (Polynomial.X ^ n - Polynomial.C a) →
        ∀ (L : Type u_1) [inst_1 : Field L] [inst_2 : Algebra K L]
          [Polynomial.IsSplittingField K L (Polynomial.X ^ n - Polynomial.C a)] [NeZero n], IsCyclic Gal(L/K)

Defined in: Mathlib.FieldTheory.KummerExtension
Cited by: 1 results in Mathlib
Foundations: Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Algebra Polynomial.IsSplittingField NeZero

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DFunLike.coestatement and proof · cited by 62,936
Algebrastatement and proof · cited by 11,388
RingHomstatement · cited by 10,189
Fieldstatement and proof · cited by 7,404
Polynomialstatement · cited by 5,681
AlgEquivstatement · cited by 1,681
Polynomial.Xstatement and proof · cited by 1,639
Polynomial.Cstatement and proof · cited by 1,598
Finset.Nonemptystatement and proof · cited by 1,001
Irreduciblestatement and proof · cited by 496
MulEquiv.symmproof · cited by 482
IsCyclicstatement · cited by 122

Cited by1

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isCyclic_tfaeproof · cited by 0