Theorems · Theorem · ring theory

IsSemisimpleModule.lifting_property

∀ {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] {P : Type u_6} [inst_6 : AddCommGroup P]
  [inst_7 : Module R P] (f : M →ₗ[R] N), Function.Surjective ⇑f → ∀ (g : P →ₗ[R] N), ∃ h, f ∘ₗ h = g

Defined in

Mathlib.RingTheory.SimpleModule.Basic

Cited by

1 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddCommGroupModuleIsSemisimpleModuleAddCommGroupModule