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Theorems · Theorem · field theory

IsPurelyInseparable.finSepDegree_eq_one

∀ (F : Type u) (E : Type v) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] [IsPurelyInseparable F E],
  Field.finSepDegree F E = 1

A purely inseparable extension has finite separable degree one.

Defined in
Mathlib.FieldTheory.PurelyInseparable.Basic
Cited by
2 results in Mathlib
Foundations
Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldFieldAlgebraIsPurelyInseparable
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isPurelyInseparable_iff_finSepDegree_eq_one · cited by 2isPurelyInseparable_iff_f…Field.finSepDegree_eq · cited by 2Field.finSepDegree_eqAlgebra · cited by 11388AlgebraField · cited by 7404FieldIsPurelyInseparable · cited by 84IsPurelyInseparableField.finSepDegree · cited by 24Field.finSepDegreeNat.card_unique · cited by 8Nat.card_uniqueIsPurelyInseparable.finSepDeg…CITED BYCITES

Cites5

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Cited by2

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