Theorems · Theorem · group theory

Representation.mem_invtSubmodule

∀ {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},
  p ∈ ρ.invtSubmodule ↔ ∀ (g : G), p ∈ Module.End.invtSubmodule (ρ g)

Defined in

Mathlib.RepresentationTheory.Submodule

Cited by

1 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringMonoidAddCommMonoidModule