Theorems · Theorem · ring theory

IsSemisimpleModule.of_injective

∀ {R : Type u_2} [inst : Ring R] {M : Type u_4} [inst_1 : AddCommGroup M] [inst_2 : Module R M] {N : Type u_5}
  [inst_3 : AddCommGroup N] [inst_4 : Module R N] [IsSemisimpleModule R M] (f : N →ₗ[R] M),
  Function.Injective ⇑f → IsSemisimpleModule R N

Defined in

Mathlib.RingTheory.SimpleModule.Basic

Cited by

2 results in Mathlib

Foundations

Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddCommGroupModuleIsSemisimpleModule