Theorems · Theorem · field theory
AlgEquiv.liftNormal_commutes
∀ {F : Type u_1} [inst : Field F] {K₁ : Type u_3} {K₂ : Type u_4} [inst_1 : Field K₁] [inst_2 : Field K₂]
[inst_3 : Algebra F K₁] [inst_4 : Algebra F K₂] (χ : K₁ ≃ₐ[F] K₂) (E : Type u_6) [inst_5 : Field E]
[inst_6 : Algebra F E] [inst_7 : Algebra K₁ E] [inst_8 : Algebra K₂ E] [inst_9 : IsScalarTower F K₁ E]
[inst_10 : IsScalarTower F K₂ E] [inst_11 : Normal F E] (x : K₁),
(χ.liftNormal E) ((algebraMap K₁ E) x) = (algebraMap K₂ E) (χ x)- Defined in
- Mathlib.FieldTheory.Normal.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapstatement · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- AlgEquivstatement and proof · cited by 1,681
- AlgEquiv.toAlgHomproof · cited by 273
- Normalstatement and proof · cited by 92
- AlgEquiv.liftNormalstatement · cited by 6
- AlgHom.liftNormal_commutesproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- AlgEquiv.restrict_liftNormalproof · cited by 1
- minpoly.exists_algEquiv_of_rootproof · cited by 1
- InfiniteGalois.toAlgEquivAux_eq_liftNormalproof · cited by 0