Exercise 14, § 2

Let $A$ be a ring. Show that for every $A$-module $M$ there exists an injective $A$-module $I$ 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 the quotient of a free $A$-module.)