Theorems · Theorem · field theory
IntermediateField.eq_bot_of_isPurelyInseparable_of_isSeparable
∀ {F : Type u} {E : Type v} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] (L : IntermediateField F E)
[IsPurelyInseparable F ↥L] [Algebra.IsSeparable F ↥L], L = ⊥If an intermediate field of E / F is both purely inseparable and separable, then it is equal
to F.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 111 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
- Bot.botstatement · cited by 4,720
- Algebra.algebraMapproof · cited by 4,706
- IntermediateFieldstatement and proof · cited by 988
- Algebra.IsSeparablestatement and proof · cited by 210
- IsPurelyInseparablestatement and proof · cited by 84
- bot_uniqueproof · cited by 57
- IsPurelyInseparable.surjective_algebraMap_of_isSeparableproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- IntermediateField.adjoin_eq_adjoin_pow_expChar_pow_of_isSeparableproof · cited by 4
- perfectClosure.eq_bot_of_isSeparableproof · cited by 1
- separableClosure_inf_perfectClosureproof · cited by 0