Exercise 14, § 2

Let $A$ be a ring. Now prove that for every $A$-module $M$, there exists an $A$-module injective $I$ such that $M$ is isomorphic to a submodule of $I$. (Apply Exercise 13 d) with $C = \mathbf{Z}$, using Exercise 11 b) and the fact that every $A$-module is quotient of a free $A$-module.)