Theorems · Definition · field theory

rootOfSplitsXPowSubC

{K : Type u} →
  [inst : Field K] →
    {n : ℕ} →
      0 < n →
        (a : K) →
          (L : Type u_2) →
            [inst_1 : Field L] →
              [inst_2 : Algebra K L] → [Polynomial.IsSplittingField K L (Polynomial.X ^ n - Polynomial.C a)] → L

An arbitrary choice of ⁿ√a in the splitting field of Xⁿ - a.

Defined in: Mathlib.FieldTheory.KummerExtension
Cited by: 4 results in Mathlib
Foundations: Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Algebra Polynomial.IsSplittingField

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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites9

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
Fieldstatement and proof · cited by 7,404
Polynomialstatement · cited by 5,681
Polynomial.Xstatement and proof · cited by 1,639
Polynomial.Cstatement and proof · cited by 1,598
Polynomial.IsSplittingFieldstatement and proof · cited by 50
Polynomial.rootOfSplitsproof · cited by 7

Cited by4

Results whose statement or proof uses this declaration.

rootOfSplitsXPowSubC_powstatement · cited by 2
autEquivRootsOfUnity_apply_rootOfSplitstatement and proof · cited by 1
autEquivRootsOfUnity_smulproof · cited by 1
rootOfSplitsXPowSubC.congr_simpstatement and proof · cited by 0