Theorems · Theorem · field theory
separableClosure.normalClosure_eq_self
∀ (F : Type u) (E : Type v) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E], IntermediateField.normalClosure F (↥(separableClosure F E)) E = separableClosure F E
The normal closure in E/F of the separable closure of F in E is equal to itself.
- Defined in
- Mathlib.FieldTheory.SeparableClosure
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- AlgHomproof · cited by 3,236
- le_antisymmproof · cited by 2,068
- IntermediateFieldstatement · cited by 988
- Algebra.IsSeparableproof · cited by 210
- AlgHom.fieldRangeproof · cited by 57
- separableClosurestatement and proof · cited by 55
- IntermediateField.normalClosurestatement · cited by 38
- AlgEquiv.ofInjectiveFieldproof · cited by 19
- IntermediateField.le_normalClosureproof · cited by 8
- AlgEquiv.Algebra.isSeparableproof · cited by 3
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.