Theorems · Theorem · field theory
Polynomial.SplittingField.splits
∀ {K : Type v} [inst : Field K] (f : Polynomial K), (Polynomial.map (algebraMap K f.SplittingField) f).Splits[Stacks Tag 09HU](https://stacks.math.columbia.edu/tag/09HU) (Splitting part)
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 153 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.
Cites7
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
- Algebra.algebraMapstatement · cited by 4,706
- Polynomial.mapstatement · cited by 806
- Polynomial.Splitsstatement · cited by 290
- Polynomial.SplittingFieldstatement and proof · cited by 42
- Polynomial.IsSplittingField.splitsproof · cited by 14
Cited by21
Results whose statement or proof uses this declaration.
- Polynomial.induction_of_Splits_of_injective_of_surjectiveproof · cited by 4
- Polynomial.resultant_eq_prod_evalproof · cited by 3
- Field.nonempty_algHom_of_exists_rootproof · cited by 3
- GaloisField.finrankproof · cited by 2
- Polynomial.natSepDegree_eq_natDegree_iffproof · cited by 2
- Polynomial.natSepDegree_eq_of_splitsproof · cited by 2
- Polynomial.Gal.restrictDvd_defstatement · cited by 2
- Field.primitive_element_inf_auxproof · cited by 1
- Polynomial.Gal.restrictDvd_surjectiveproof · cited by 1
- Polynomial.resultant_eq_prod_roots_subproof · cited by 1
- integralClosure.mem_lifts_of_monic_of_dvd_mapproof · cited by 1
- IsAlgClosure.of_exists_rootproof · cited by 1