Theorems · Theorem · field theory

IntermediateField.LinearDisjoint.of_basis_left

∀ {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]
  {ι : Type u_1} (a : Module.Basis ι F ↥A), LinearIndependent L (⇑A.val ∘ ⇑a) → A.LinearDisjoint L

If there exists an F-basis of A which remains linearly independent over L, then A and L are linearly disjoint.

Defined in

Mathlib.FieldTheory.LinearDisjoint

Cited by

1 results in Mathlib

Foundations

Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldFieldAlgebraFieldAlgebraAlgebraIsScalarTower