Theorems · Theorem · linear algebra

ExteriorAlgebra.map_injective_field

∀ {K : Type u_1} {E : Type u_2} {F : Type u_3} [inst : Field K] [inst_1 : AddCommGroup E] [inst_2 : Module K E]
  [inst_3 : AddCommGroup F] [inst_4 : Module K F] {f : E →ₗ[K] F},
  f.ker = ⊥ → Function.Injective ⇑(ExteriorAlgebra.map f)

An injective morphism of vector spaces induces an injective morphism of exterior algebras.

Defined in

Mathlib.LinearAlgebra.ExteriorAlgebra.Basic

Cited by

0 results in Mathlib

Foundations

Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldAddCommGroupModuleAddCommGroupModule