Theorems · Theorem · field theory
AlgEquiv.restrictNormalHom_surjective
∀ {F : Type u_1} [inst : Field F] {K₁ : Type u_3} [inst_1 : Field K₁] [inst_2 : Algebra F K₁] (E : Type u_6)
[inst_3 : Field E] [inst_4 : Algebra F E] [inst_5 : Algebra K₁ E] [inst_6 : IsScalarTower F K₁ E]
[inst_7 : Normal F K₁] [Normal F E], Function.Surjective ⇑(AlgEquiv.restrictNormalHom K₁)The group homomorphism given by restricting an algebra isomorphism to a normal subfield is surjective.
- Defined in
- Mathlib.FieldTheory.Normal.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Fieldstatement and proof · cited by 7,404
- IsScalarTowerstatement and proof · cited by 3,896
- MonoidHomstatement · cited by 3,629
- AlgEquivstatement and proof · cited by 1,681
- Normalstatement and proof · cited by 92
- AlgEquiv.restrictNormalHomstatement · cited by 21
- AlgEquiv.liftNormalproof · cited by 6
- AlgEquiv.restrict_liftNormalproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- InfiniteGalois.fixedField_fixingSubgroupproof · cited by 3
- InfiniteGalois.normal_iff_isGaloisproof · cited by 2
- Polynomial.Gal.restrict_surjectiveproof · cited by 2
- IntermediateField.map_fixingSubgroup_indexproof · cited by 1
- IsGalois.finiteDimensional_of_finiteproof · cited by 1
- gal_isSolvable_of_splitsproof · cited by 0