Theorems · Theorem · field theory

IntermediateField.adjoin_root_eq_top_of_isSplittingField

∀ {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)] {α : L},
          α ^ n = (algebraMap K L) a → K⟮α⟯ = ⊤

Defined in: Mathlib.FieldTheory.KummerExtension
Cited by: 0 results in Mathlib
Foundations: Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Algebra Polynomial.IsSplittingField

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites18

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
Setstatement · cited by 53,352
Algebrastatement and proof · cited by 11,388
RingHomstatement · cited by 10,189
Top.topstatement and proof · cited by 9,680
Fieldstatement and proof · cited by 7,404
Polynomialstatement · cited by 5,681
Algebra.algebraMapstatement and proof · cited by 4,706
Polynomial.Xstatement and proof · cited by 1,639
Polynomial.Cstatement and proof · cited by 1,598
Finset.Nonemptystatement and proof · cited by 1,001
IntermediateFieldstatement · cited by 988

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.