Theorems · Definition · field theory
Polynomial.Gal.restrict
{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] → Gal(E/F) →* p.GalRestrict from a superfield automorphism into a member of gal p.
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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 and proof · cited by 4,706
- MonoidHomstatement · cited by 3,629
- Factstatement and proof · cited by 2,726
- AlgEquivstatement · cited by 1,681
- Polynomial.mapstatement and proof · cited by 806
- Polynomial.Splitsstatement and proof · cited by 290
- Polynomial.SplittingFieldproof · cited by 42
- Polynomial.Galstatement · cited by 37
- AlgEquiv.restrictNormalHomproof · cited by 21
Cited by12
Results whose statement or proof uses this declaration.
- Polynomial.Gal.restrictDvdproof · cited by 3
- Polynomial.Gal.restrictDvd_defstatement and proof · cited by 2
- Polynomial.Gal.restrict_surjectivestatement · cited by 2
- Polynomial.Gal.card_complex_roots_eq_card_real_add_card_not_gal_invstatement and proof · cited by 2
- Polynomial.Gal.galActionHom_bijective_of_prime_degreeproof · cited by 1
- Polynomial.Gal.galActionHom_restrictstatement · cited by 1
- Polynomial.Gal.restrictCompproof · cited by 1
- Polynomial.Gal.restrictDvd_surjectiveproof · cited by 1
- Polynomial.Gal.restrictProd_injectiveproof · cited by 1
- Polynomial.Gal.restrict_smulstatement · cited by 1
- Polynomial.Gal.restrict.congr_simpstatement and proof · cited by 0
- Polynomial.Gal.galActionHom_bijective_of_prime_degree'proof · cited by 0