Example 1

If A is integral, the field of fractions K of A is an A-module injective. If A is principal, $K/A$ is an A-module injective. 2) For example, the $\mathbf{Z}$-modules $\mathbf{Q}$ and $\mathbf{Q}/\mathbf{Z}$ are injective. 3) Let A be a principal ideal domain and let $a$ be a nonzero element of A. Then $A/aA$ is an $A/aA$-module injective (X, p. 170, exercise 20).