Theorems · Theorem · field theory
le_perfectClosure_iff
∀ (F : Type u) (E : Type v) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] (L : IntermediateField F E), L ≤ perfectClosure F E ↔ IsPurelyInseparable F ↥L
An intermediate field of E / F is contained in the relative perfect closure of F in E
if and only if it is purely inseparable over F.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- RingHom.injectiveproof · cited by 187
- IsPurelyInseparablestatement and proof · cited by 84
- RingHom.rangeSproof · cited by 47
- ringExpCharproof · cited by 27
- perfectClosurestatement and proof · cited by 14
- isPurelyInseparable_iff_pow_memproof · cited by 10
- le_perfectClosureproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- IntermediateField.isPurelyInseparable_adjoin_simple_iff_pow_memproof · cited by 1