Theorems · Theorem · group theory

Representation.asAlgebraHom_mem_of_forall_mem

∀ {k : Type u_1} {G : Type u_2} {V : Type u_3} [inst : CommSemiring k] [inst_1 : Monoid G] [inst_2 : AddCommMonoid V]
  [inst_3 : Module k V] (ρ : Representation k G V) (p : Submodule k V),
  (∀ (g : G), ∀ v ∈ p, (ρ g) v ∈ p) → ∀ v ∈ p, ∀ (x : MonoidAlgebra k G), (ρ.asAlgebraHom x) v ∈ p

Defined in

Mathlib.RepresentationTheory.Submodule

Cited by

0 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringMonoidAddCommMonoidModule