Theorems · Definition · field theory
Polynomial.Gal.rootsEquivRoots
{F : Type u_1} →
[inst : Field F] →
(p : Polynomial F) →
(E : Type u_2) →
[inst_1 : Field E] →
[inst_2 : Algebra F E] →
[Fact (Polynomial.map (algebraMap F E) p).Splits] → ↑(p.rootSet p.SplittingField) ≃ ↑(p.rootSet E)The bijection between rootSet p p.SplittingField and rootSet p E.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Equivstatement · cited by 8,337
- Fieldstatement and proof · cited by 7,404
- Set.Elemstatement · cited by 7,166
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapstatement and proof · cited by 4,706
- Factstatement and proof · cited by 2,726
- Polynomial.mapstatement and proof · cited by 806
- Polynomial.Splitsstatement and proof · cited by 290
- Polynomial.rootSetstatement · cited by 101
- Equiv.ofBijectiveproof · cited by 70
- Polynomial.SplittingFieldstatement · cited by 42
Cited by6
Results whose statement or proof uses this declaration.
- Polynomial.Gal.restrict_smulproof · cited by 1
- Polynomial.Gal.galActionHom_injectiveproof · cited by 1
- Polynomial.Gal.restrictProd_injectiveproof · cited by 1
- Polynomial.Gal.galAction_isPretransitiveproof · cited by 0
- Polynomial.Gal.rootsEquivRoots.congr_simpstatement and proof · cited by 0
- Polynomial.Gal.smul_defstatement · cited by 0