Theorems · Theorem · field theory
separableClosure_le
∀ (F : Type u) (E : Type v) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] (L : IntermediateField F E) [h : IsPurelyInseparable (↥L) E], separableClosure F E ≤ L
An intermediate field of E / F contains the separable closure of F in E
if E is purely inseparable over it.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Algebra.algebraMapproof · cited by 4,706
- IntermediateFieldstatement and proof · cited by 988
- IsPurelyInseparablestatement and proof · cited by 84
- separableClosurestatement and proof · cited by 55
- IsSeparable.tower_topproof · cited by 11
- mem_separableClosure_iffproof · cited by 7
- IsPurelyInseparable.inseparable'proof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- eq_separableClosureproof · cited by 1
- separableClosure_le_iffproof · cited by 0