Theorems · Theorem · field theory
AlgEquiv.restrictNormalHom_id
∀ (F : Type u_6) (K : Type u_7) [inst : Field F] [inst_1 : Field K] [inst_2 : Algebra F K] [inst_3 : Normal F K], AlgEquiv.restrictNormalHom K = MonoidHom.id Gal(K/F)
The group homomorphism given by restricting an algebra isomorphism to itself is the identity map.
- Defined in
- Mathlib.FieldTheory.Normal.Defs
- Cited by
- 1 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapproof · cited by 4,706
- MonoidHomstatement · cited by 3,629
- AlgEquivstatement and proof · cited by 1,681
- MonoidHom.idstatement · cited by 323
- RingHom.injectiveproof · cited by 187
- MonoidHom.extproof · cited by 109
- Normalstatement and proof · cited by 92
- AlgEquiv.extproof · cited by 60
- AlgEquiv.restrictNormalHomstatement · cited by 21
Cited by1
Results whose statement or proof uses this declaration.
- finGaloisGroupMap.map_idproof · cited by 0