Theorems · Theorem · field theory
Polynomial.IsSplittingField.splits
∀ {K : Type v} (L : Type w) [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L] (f : Polynomial K)
[Polynomial.IsSplittingField K L f], (Polynomial.map (algebraMap K L) f).Splits- Cited by
- 14 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapstatement · cited by 4,706
- Polynomial.mapstatement · cited by 806
- Polynomial.Splitsstatement · cited by 290
- Polynomial.IsSplittingFieldstatement and proof · cited by 50
- Polynomial.IsSplittingField.splits'proof · cited by 2
Cited by14
Results whose statement or proof uses this declaration.
- Polynomial.SplittingField.splitsproof · cited by 21
- FiniteField.nonempty_algHom_of_finrank_dvdproof · cited by 3
- Polynomial.IsSplittingField.IsScalarTower.splitsproof · cited by 2
- rootOfSplitsXPowSubC_powproof · cited by 2
- Polynomial.IsSplittingField.adjoin_rootSet_eq_rangeproof · cited by 1
- Irreducible.natDegree_dvd_of_dvd_X_pow_card_pow_sub_Xproof · cited by 1
- FiniteField.splits_X_pow_card_sub_Xproof · cited by 0
- FiniteField.splits_X_pow_nat_card_sub_Xproof · cited by 0
- Polynomial.IsSplittingField.mulproof · cited by 0
- IsGalois.of_separable_splitting_field_auxproof · cited by 0
- Polynomial.Gal.mapRoots_bijectiveproof · cited by 0
- Polynomial.IsSplittingField.of_algEquivproof · cited by 0