Theorems · Theorem · ring theory

Module.Injective.extension_property

∀ (R : Type uR) [inst : Ring R] [Small.{uM, uR} R] (M : Type uM) [inst_2 : AddCommGroup M] [inst_3 : Module R M]
  [inj : Module.Injective R M] (P : Type uP) [inst_4 : AddCommGroup P] [inst_5 : Module R P] (P' : Type uP')
  [inst_6 : AddCommGroup P'] [inst_7 : Module R P'] (f : P →ₗ[R] P'),
  Function.Injective ⇑f → ∀ (g : P →ₗ[R] M), ∃ h, h ∘ₗ f = g

Defined in

Mathlib.Algebra.Module.Injective

Cited by

0 results in Mathlib

Foundations

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

Assumes

RingSmallAddCommGroupModuleModule.InjectiveAddCommGroupModuleAddCommGroupModule