Theorems · Theorem · field theory

IntermediateField.LinearDisjoint.of_isField

∀ {F : Type u} {E : Type v} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] {A : IntermediateField F E}
  {L : Type w} [inst_3 : Field L] [inst_4 : Algebra F L] [inst_5 : Algebra L E] [inst_6 : IsScalarTower F L E],
  IsField (TensorProduct F (↥A) L) → A.LinearDisjoint L

If A ⊗[F] L is a field, then A and L are linearly disjoint over F.

Defined in

Mathlib.FieldTheory.LinearDisjoint

Cited by

1 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldFieldAlgebraFieldAlgebraAlgebraIsScalarTower