Theorems · Theorem · field theory

IntermediateField.LinearDisjoint.norm_algebraMap

∀ {F : Type u} {E : Type v} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] {A B : IntermediateField F E}
  [FiniteDimensional F E],
  A.LinearDisjoint ↥B →
    A ⊔ B = ⊤ → ∀ (x : ↥B), (Algebra.norm ↥A) ((algebraMap (↥B) E) x) = (algebraMap F ↥A) ((Algebra.norm F) x)

If A and B are linearly disjoint, then norm and algebraMap commutes.

Defined in

Mathlib.FieldTheory.LinearDisjoint

Cited by

0 results in Mathlib

Foundations

Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldFieldAlgebraFiniteDimensional