Theorems · Theorem · field theory
FixedPoints.toAlgAut_bijective
∀ (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], Function.Bijective ⇑(MulSemiringAction.toAlgAut G (↥(FixedPoints.subfield G F)) F)
MulSemiringAction.toAlgAut is bijective.
- 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.
Cites18
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
- Fieldstatement and proof · cited by 7,404
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement · cited by 3,629
- Finitestatement and proof · cited by 3,029
- AlgEquivstatement and proof · cited by 1,681
- Function.Bijectivestatement · cited by 863
- MulSemiringActionstatement and proof · cited by 423
- FaithfulSMulstatement and proof · cited by 340
- Subfieldstatement · cited by 303
- AlgEquiv.toAlgHomproof · cited by 273
- Function.Bijective.injectiveproof · cited by 115
Cited by2
Results whose statement or proof uses this declaration.
- FixedPoints.toAlgAut_surjectiveproof · cited by 1
- FixedPoints.toAlgAutMulEquivproof · cited by 0