Theorems · Definition · field theory
FixedPoints.toAlgHomEquiv
(G : Type u_2) →
(F : Type u_3) →
[inst : Group G] →
[inst_1 : Field F] →
[inst_2 : MulSemiringAction G F] → [Finite G] → [FaithfulSMul G F] → G ≃ (F →ₐ[↥(FixedPoints.subfield G F)] F)Bijection between G and algebra endomorphisms of F that fix the fixed points.
- Defined in
- Mathlib.FieldTheory.Fixed
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivstatement · cited by 8,337
- Fieldstatement and proof · cited by 7,404
- Groupstatement and proof · cited by 6,238
- AlgHomstatement · cited by 3,236
- Finitestatement and proof · cited by 3,029
- MulSemiringActionstatement and proof · cited by 423
- FaithfulSMulstatement and proof · cited by 340
- Subfieldstatement · cited by 303
- Equiv.ofBijectiveproof · cited by 70
- FixedPoints.subfieldstatement and proof · cited by 20
- MulSemiringAction.toAlgHomproof · cited by 10
- FixedPoints.toAlgHom_bijectiveproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IntermediateField.fixingSubgroup_fixedFieldproof · cited by 3