Theorems · Definition · field theory
fixedByFinite
(K : Type u_1) → (L : Type u_2) → [inst : Field K] → [inst_1 : Field L] → [inst_2 : Algebra K L] → Set (Subgroup Gal(L/K))
Given a field extension L/K, fixedByFinite K L is the set of
subsets Gal(L/E) of Gal(L/K), where E/K is finite.
- Defined in
- Mathlib.FieldTheory.KrullTopology
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Set.imageproof · cited by 5,609
- Subgroupstatement · cited by 3,593
- AlgEquivstatement · cited by 1,681
- IntermediateField.fixingSubgroupproof · cited by 41
- finiteExtsproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- krullTopology_mem_nhds_one_iffproof · cited by 2
- galBasisproof · cited by 1
- InfiniteGalois.isOpen_iff_finiteproof · cited by 1
- mem_galBasis_iffstatement · cited by 0
- InfiniteGalois.fixingSubgroup_fixedFieldproof · cited by 0
- top_fixedByFinitestatement · cited by 0