Theorems · Theorem · field theory
AlgHom.restrictNormal_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] (ϕ : K₁ →ₐ[F] K₂) (E : Type u_6) [inst_5 : Field E]
[inst_6 : Algebra F E] [inst_7 : Algebra E K₁] [inst_8 : Algebra E K₂] [inst_9 : IsScalarTower F E K₁]
[inst_10 : IsScalarTower F E K₂] [inst_11 : Normal F E] (x : E),
(algebraMap E K₂) ((ϕ.restrictNormal E) x) = ϕ ((algebraMap E K₁) x)- Defined in
- Mathlib.FieldTheory.Normal.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 146 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- 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
- AlgHomstatement and proof · cited by 3,236
- IsScalarTower.toAlgHomproof · cited by 232
- Normalstatement and proof · cited by 92
- AlgEquiv.apply_symm_applyproof · cited by 67
- AlgEquiv.ofInjectiveFieldproof · cited by 19
- AlgHom.restrictNormalstatement · cited by 4
Cited by9
Results whose statement or proof uses this declaration.
- AlgEquiv.restrictNormal_commutesproof · cited by 13
- Algebra.norm_eq_prod_automorphismsproof · cited by 5
- AlgHom.fieldRange_of_normalproof · cited by 2
- IntermediateField.normalClosure_def''proof · cited by 2
- NumberField.ComplexEmbedding.exists_comp_symm_eq_of_comp_eqproof · cited by 1
- NumberField.InfinitePlace.isUnramified_mk_iff_forall_isConjproof · cited by 1
- trace_eq_sum_automorphismsproof · cited by 1
- AlgHom.restrict_liftNormalproof · cited by 0
- AlgHom.restrictNormal_compproof · cited by 0