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Theorems · Theorem · field theory

IsPurelyInseparable.trans

∀ (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] [h1 : IsPurelyInseparable F E]
  [h2 : IsPurelyInseparable E K], IsPurelyInseparable F K

If E / F and K / E are both purely inseparable extensions, then K / F is also purely inseparable.

Defined in
Mathlib.FieldTheory.PurelyInseparable.Basic
Cited by
1 results in Mathlib
Foundations
Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldFieldAlgebraFieldAlgebraAlgebraIsScalarTowerIsPurelyInseparableIsPurelyInseparable
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

RingHom.IsPurelyInseparable.comp · cited by 0IsPurelyInseparable.compDFunLike.coe · cited by 62936DFunLike.coeAlgebra · cited by 11388AlgebraField · cited by 7404FieldAlgebra.algebraMap · cited by 4706Algebra.algebraMapIsScalarTower · cited by 3896IsScalarTowermap_pow · cited by 503map_powpow_add · cited by 315pow_addExpChar · cited by 276ExpCharpow_mul · cited by 210pow_mulRingHom.injective · cited by 187RingHom.injectiveRingHom.range · cited by 138RingHom.rangeIsScalarTower.algebraMap_apply · cited by 116IsScalarTower.algebraMap_…IsPurelyInseparable · cited by 84IsPurelyInseparableExpChar.exists · cited by 11ExpChar.existsisPurelyInseparable_iff_pow_mem · cited by 10isPurelyInseparable_iff_p…IsPurelyInseparable.transCITED BYCITES

Cites16

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Cited by1

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