Theorems · Definition · field theory
Polynomial.SplittingField
{K : Type v} → [inst : Field K] → Polynomial K → Type vA splitting field of a polynomial.
- Cited by
- 42 results in Mathlib
- Foundations
- Depth 133 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- HasQuotient.Quotientproof · cited by 2,301
- MvPolynomialproof · cited by 2,140
- Polynomial.natDegreeproof · cited by 1,105
- AlgHom.toRingHomproof · cited by 490
- RingHom.kerproof · cited by 363
- MvPolynomial.aevalproof · cited by 298
- Polynomial.SplittingFieldAuxproof · cited by 4
Cited by55
Results whose statement or proof uses this declaration.
- Polynomial.natSepDegreeproof · cited by 53
- Polynomial.Galproof · cited by 37
- Polynomial.SplittingField.splitsstatement and proof · cited by 21
- CyclotomicFieldproof · cited by 14
- Polynomial.Gal.restrictproof · cited by 10
- Polynomial.Gal.rootsEquivRootsstatement · cited by 6
- GaloisFieldproof · cited by 5
- Polynomial.Gal.extstatement and proof · cited by 5
- Polynomial.natSepDegree_X_sub_Cproof · cited by 4
- Polynomial.induction_of_Splits_of_injective_of_surjectiveproof · cited by 4
- Polynomial.resultant_eq_prod_evalproof · cited by 3
- Polynomial.Gal.restrictDvdproof · cited by 3