Theorems · Theorem · field theory
Polynomial.Gal.galActionHom_injective
∀ {F : Type u_1} [inst : Field F] (p : Polynomial F) (E : Type u_2) [inst_1 : Field E] [inst_2 : Algebra F E]
[inst_3 : Fact (Polynomial.map (algebraMap F E) p).Splits], Function.Injective ⇑(Polynomial.Gal.galActionHom p E)gal p embeds as a subgroup of permutations of the roots of p in E.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Set.Elemstatement and proof · cited by 7,166
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapstatement and proof · cited by 4,706
- Equiv.symmproof · cited by 3,681
- MonoidHomstatement · cited by 3,629
- Factstatement and proof · cited by 2,726
- Equiv.Permstatement · cited by 1,375
- Polynomial.mapstatement and proof · cited by 806
- Equiv.injectiveproof · cited by 464
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.Gal.galActionHom_bijective_of_prime_degreeproof · cited by 1