Theorems · Theorem · ring theory

IsIsotypic.linearEquiv_fun

∀ {R : Type u_2} {M : Type u} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [IsSemisimpleModule R M]
  [Module.Finite R M] [Nontrivial M],
  IsIsotypic R M → ∃ n, ∃ (_ : NeZero n), ∃ S, IsSimpleModule R ↥S ∧ Nonempty (M ≃ₗ[R] Fin n → ↥S)

Defined in

Mathlib.RingTheory.SimpleModule.Isotypic

Cited by

3 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleIsSemisimpleModuleModule.FiniteNontrivial