Theorems · Theorem · ring theory

isIsotypicOfType_submodule_iff

∀ {R : Type u_2} {M : Type u} {S : Type u_4} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : AddCommGroup S]
  [inst_3 : Module R M] [inst_4 : Module R S] {N : Submodule R M},
  IsIsotypicOfType R (↥N) S ↔ ∀ m ≤ N, ∀ [IsSimpleModule R ↥m], Nonempty (↥m ≃ₗ[R] S)

Defined in

Mathlib.RingTheory.SimpleModule.Isotypic

Cited by

4 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupAddCommGroupModuleModule