2

Definition: An $R$-module $M$ is called quasi-injective module if for every submodule $N$, any $R$-homomorphism $N\to M$ extends to an endomorphism of $M$.

How can I prove that every injective module is quasi-injective ?

amWhy
  • 209,954
Adam Ben
  • 37
  • 3
  • Could you solve the problem with the hint I've done? If yes, would you like to accept the answer to remove the question off the "unanswered queue"? If no, tell me and I'll try to expand the hint to an answer – Alejandro Tolcachier Feb 03 '20 at 14:23

1 Answers1

1

Hint: Use the definition of the injectivity in the case of $\iota:N\to M$ being the inclusion.

Alejandro Tolcachier
  • 1,938