Exercise 3, § 7

Give an example of a ring A with the following property: in the A-module $E = A^2$, there exists a submodule F such that, if $j : F \to E$ is the canonical injection, $\bigwedge^2 j$ is identically zero even when neither $\bigwedge^2 E$ nor $\bigwedge^2 F$ reduces to 0 (II, § 4, Exercise 2).