Theorems · Definition · field theory
InfiniteGalois.IntermediateFieldEquivClosedSubgroup
{k : Type u_1} →
{K : Type u_2} →
[inst : Field k] →
[inst_1 : Field K] →
[inst_2 : Algebra k K] → [IsGalois k K] → IntermediateField k K ≃o (ClosedSubgroup Gal(K/k))ᵒᵈThe Galois correspondence from intermediate fields to closed subgroups.
- Defined in
- Mathlib.FieldTheory.Galois.Infinite
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- AlgEquivstatement and proof · cited by 1,681
- IntermediateFieldstatement and proof · cited by 988
- OrderDualstatement and proof · cited by 927
- OrderIsostatement · cited by 874
- IsGaloisstatement and proof · cited by 149
- IntermediateField.fixingSubgroupproof · cited by 41
- IntermediateField.fixedFieldproof · cited by 25
- ClosedSubgroupstatement and proof · cited by 11
- ClosedSubgroup.toSubgroupproof · cited by 8
- InfiniteGalois.fixedField_fixingSubgroupproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- InfiniteGalois.isOpen_iff_finiteproof · cited by 1
- InfiniteGalois.GaloisInsertionIntermediateFieldClosedSubgroupproof · cited by 0