Theorems · Theorem · ring theory

le_isotypicComponent_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] [IsSimpleModule R S] [IsSemisimpleModule R M] {m : Submodule R M},
  m ≤ isotypicComponent R M S ↔ IsIsotypicOfType R (↥m) S

Defined in

Mathlib.RingTheory.SimpleModule.Isotypic

Cited by

2 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupAddCommGroupModuleModuleIsSimpleModuleIsSemisimpleModule