Exercise 24, § 2

Let $M$ be an $A$-module, $I$ its injective envelope (Exercise 18), $a$ a two-sided ideal of $A$ and $Q$ the submodule of $I$ consisting of the $z \in I$ such that $az = \{0\}$; $Q$ has a natural $(A/a)$-module structure. Let $N$ be the submodule of $M$ consisting of the $x \in M$ such that $ax = \{0\}$; if $N$ is considered as an $(A/a)$-module, show that $Q$ is isomorphic to an injective envelope of $N$.