I am having trouble coming up with an example to an old exam I am using to help study for some linear algebra qualifiers.
Let $R$ be commutative ring and set $M = R \times R$. Considering $M^2$ as a $R$ module is there an example of a surjective $R$-module homomorphism from $f: M^2 \rightarrow M$ so that the matrix corresponding to the linear transformation $f$ contains only entries which are divisors of zero.