Theorems · Theorem · field theory
IntermediateField.linearDisjoint_of_isPurelyInseparable_of_isSeparable
∀ {F : Type u} (E : Type v) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] {K : Type w} [inst_3 : Field K]
[inst_4 : Algebra F K] [inst_5 : Algebra E K] [inst_6 : IsScalarTower F E K] [IsPurelyInseparable F E]
(S : IntermediateField F K) [Algebra.IsSeparable F ↥S], S.LinearDisjoint EIf K / E / F is a field extension tower such that E / F is purely inseparable,
if S is an intermediate field of K / F which is separable over F, then S and E are
linearly disjoint over F.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Set.Elemproof · cited by 7,166
- IsScalarTowerstatement and proof · cited by 3,896
- Module.Basisproof · cited by 1,477
- IntermediateFieldstatement and proof · cited by 988
- AlgHom.toRingHomproof · cited by 490
- AlgHom.toLinearMapproof · cited by 254
- Algebra.IsSeparablestatement and proof · cited by 210
- RingHom.injectiveproof · cited by 187
Cited by2
Results whose statement or proof uses this declaration.
- Field.lift_rank_mul_lift_insepDegree_of_isPurelyInseparableproof · cited by 2
- Field.sepDegree_eq_of_isPurelyInseparable_of_isSeparableproof · cited by 1