Theorems · Theorem · ring theory

Submodule.le_linearEquiv_of_sSup_eq_top

∀ {R : Type u_2} {M : Type u} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (N : Submodule R M)
  [IsSimpleModule R ↥N] (s : Set (Submodule R M)) [IsSemisimpleModule R M],
  sSup s = ⊤ → ∃ m ∈ s, ∃ S ≤ m, Nonempty (↥N ≃ₗ[R] ↥S)

Defined in

Mathlib.RingTheory.SimpleModule.Isotypic

Cited by

2 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleIsSimpleModuleIsSemisimpleModule