Theorems · Theorem · field theory
FixedPoints.toAlgHom_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.toAlgHom (↥(FixedPoints.subfield G F)) F)
MulSemiringAction.toAlgHom is bijective.
- Defined in
- Mathlib.FieldTheory.Fixed
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypeproof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- Groupstatement and proof · cited by 6,238
- AlgHomstatement and proof · cited by 3,236
- Finitestatement and proof · cited by 3,029
- le_antisymmproof · cited by 2,068
- Fintype.cardproof · cited by 1,386
- Function.Bijectivestatement · cited by 863
- MulSemiringActionstatement and proof · cited by 423
- FaithfulSMulstatement and proof · cited by 340
- LE.le.trans_eqproof · cited by 328
- Subfieldstatement · cited by 303
Cited by2
Results whose statement or proof uses this declaration.
- FixedPoints.toAlgAut_bijectiveproof · cited by 1
- FixedPoints.toAlgHomEquivproof · cited by 1