Theorems · Theorem · field theory

Field.sepDegree_mul_sepDegree_of_isAlgebraic

∀ (F : Type u) (E : Type v) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] (K : Type v) [inst_3 : Field K]
  [inst_4 : Algebra F K] [inst_5 : Algebra E K] [IsScalarTower F E K] [Algebra.IsAlgebraic F E],
  Field.sepDegree F E * Field.sepDegree E K = Field.sepDegree F K

The same-universe version of Field.lift_sepDegree_mul_lift_sepDegree_of_isAlgebraic.

Defined in: Mathlib.FieldTheory.PurelyInseparable.Tower
Cited by: 1 results in Mathlib
Foundations: Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Algebra Field Algebra Algebra IsScalarTower Algebra.IsAlgebraic

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Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Algebrastatement and proof · cited by 11,388
Fieldstatement and proof · cited by 7,404
IsScalarTowerstatement and proof · cited by 3,896
Cardinalstatement · cited by 2,598
Algebra.IsAlgebraicstatement and proof · cited by 322
Cardinal.lift_idproof · cited by 163
Field.sepDegreestatement and proof · cited by 24
Field.lift_sepDegree_mul_lift_sepDegree_of_isAlgebraicproof · cited by 2

Cited by1

Results whose statement or proof uses this declaration.

IntermediateField.sepDegree_adjoin_eq_of_isAlgebraic_of_isPurelyInseparableproof · cited by 2