Theorems · Definition · field theory
IsGalois.intermediateFieldEquivSubgroup
{F : Type u_1} →
[inst : Field F] →
{E : Type u_2} →
[inst_1 : Field E] →
[inst_2 : Algebra F E] →
[FiniteDimensional F E] → [IsGalois F E] → IntermediateField F E ≃o (Subgroup Gal(E/F))ᵒᵈThe Galois correspondence from intermediate fields to subgroups.
- Defined in
- Mathlib.FieldTheory.Galois.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Subgroupstatement and proof · cited by 3,593
- FiniteDimensionalstatement and proof · cited by 1,854
- AlgEquivstatement and proof · cited by 1,681
- IntermediateFieldstatement and proof · cited by 988
- OrderDualstatement and proof · cited by 927
- OrderIsostatement · cited by 874
- OrderDual.toDualproof · cited by 481
- OrderDual.ofDualproof · cited by 400
- IsGaloisstatement and proof · cited by 149
Cited by13
Results whose statement or proof uses this declaration.
- IsGaloisGroup.intermediateFieldEquivSubgroupproof · cited by 6
- IsCyclotomicExtension.Rat.intermediateFieldEquivSubgroupCharproof · cited by 4
- IsGalois.intermediateFieldEquivSubgroup_applystatement and proof · cited by 3
- IsGaloisGroup.intermediateFieldEquivSubgroup_symm_applyproof · cited by 2
- IsGalois.tfaeproof · cited by 2
- exists_root_adjoin_eq_top_of_isCyclicproof · cited by 1
- IsCyclotomicExtension.Rat.card_intermediateFieldEquivSubgroupCharproof · cited by 0
- IsGalois.ofDual_intermediateFieldEquivSubgroup_applystatement · cited by 0
- IsGalois.fixedField_eq_iff_fixingSubgroup_eqproof · cited by 0
- IsGalois.galoisCoinsertionIntermediateFieldSubgroupproof · cited by 0
- IsGalois.intermediateFieldEquivSubgroup_symm_applystatement · cited by 0
- IsGalois.intermediateFieldEquivSubgroup_symm_apply_toDualstatement · cited by 0