Theorems · Theorem · field theory
eq_separableClosure
∀ (F : Type u) (E : Type v) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] (L : IntermediateField F E) [Algebra.IsSeparable F ↥L] [IsPurelyInseparable (↥L) E], L = separableClosure F E
If an intermediate field of E / F is separable over F, and E is purely inseparable
over it, then it is equal to the separable closure of F in E.
- Cited by
- 1 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.
Cites9
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
- le_antisymmproof · cited by 2,068
- IntermediateFieldstatement and proof · cited by 988
- Algebra.IsSeparablestatement and proof · cited by 210
- IsPurelyInseparablestatement and proof · cited by 84
- separableClosurestatement · cited by 55
- separableClosure_leproof · cited by 2
- le_separableClosureproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- eq_separableClosure_iffproof · cited by 0