Theorems · Theorem · field theory
isSplittingField_AdjoinRoot_X_pow_sub_C
∀ {K : Type u} [inst : Field K] {n : ℕ},
(primitiveRoots n K).Nonempty →
∀ {a : K} (H : Irreducible (Polynomial.X ^ n - Polynomial.C a)),
Polynomial.IsSplittingField K (AdjoinRoot (Polynomial.X ^ n - Polynomial.C a)) (Polynomial.X ^ n - Polynomial.C a)- Defined in
- Mathlib.FieldTheory.KummerExtension
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites40
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 and proof · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- Factproof · cited by 2,726
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- Subalgebraproof · cited by 1,353
- Finset.Nonemptystatement and proof · cited by 1,001
- Polynomial.mapproof · cited by 806
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.