Theorems · Theorem · field theory
Polynomial.Gal.restrict_smul
∀ {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] (ϕ : Gal(E/F)) (x : ↑(p.rootSet E)),
↑((Polynomial.Gal.restrict p E) ϕ • x) = ϕ ↑xPolynomial.Gal.restrict p E is compatible with Polynomial.Gal.galAction p E.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
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
- Setstatement · cited by 53,352
- 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
- AlgEquivstatement and proof · cited by 1,681
- Polynomial.mapstatement and proof · cited by 806
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.Gal.galActionHom_restrictproof · cited by 1