Theorems · Theorem · field theory
IsPurelyInseparable.tower_bot
∀ (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] [IsScalarTower F E K] [IsPurelyInseparable F K], IsPurelyInseparable F E
If K / E / F is a field extension tower such that K / F is purely inseparable,
then E / F is also purely inseparable.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Polynomialproof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- RingHom.injectiveproof · cited by 187
- Polynomial.Separableproof · cited by 117
- IsScalarTower.algebraMap_applyproof · cited by 116
- IsPurelyInseparablestatement and proof · cited by 84
- IsSeparableproof · cited by 68
- minpoly.algebraMap_eqproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- isPurelyInseparable_iff_fd_isPurelyInseparableproof · cited by 0