Theorems · Theorem · field theory

IntermediateField.LinearDisjoint.linearIndependent_right

∀ {F : Type u} {E : Type v} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] {A B : IntermediateField F E},
  A.LinearDisjoint ↥B → ∀ {ι : Type u_1} {b : ι → ↥B}, LinearIndependent F b → LinearIndependent (↥A) (⇑B.val ∘ b)

If A and B are linearly disjoint, then any F-linearly independent family on B remains linearly independent over A.

Defined in

Mathlib.FieldTheory.LinearDisjoint

Cited by

0 results in Mathlib

Foundations

Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldFieldAlgebra