Theorems · Theorem · field theory
AlgEquiv.restrictNormalHom_apply
∀ {F : Type u_1} [inst : Field F] {K₁ : Type u_3} [inst_1 : Field K₁] [inst_2 : Algebra F K₁]
(L : IntermediateField F K₁) [inst_3 : Normal F ↥L] (σ : Gal(K₁/F)) (x : ↥L),
↑(((AlgEquiv.restrictNormalHom ↥L) σ) x) = σ ↑x- Defined in
- Mathlib.FieldTheory.Normal.Defs
- Cited by
- 5 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.
Cites9
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
- MonoidHomstatement · cited by 3,629
- AlgEquivstatement and proof · cited by 1,681
- IntermediateFieldstatement and proof · cited by 988
- Normalstatement and proof · cited by 92
- AlgEquiv.restrictNormalHomstatement · cited by 21
- AlgEquiv.restrictNormal_commutesproof · cited by 13
Cited by5
Results whose statement or proof uses this declaration.
- InfiniteGalois.fixedField_fixingSubgroupproof · cited by 3
- IntermediateField.restrictRestrictAlgEquivMapHom_applyproof · cited by 2
- IntermediateField.restrictNormalHom_kerproof · cited by 1
- FiniteGaloisIntermediateField.mem_fixingSubgroup_iffproof · cited by 1
- InfiniteGalois.fixingSubgroup_fixedFieldproof · cited by 0