Exercise 1, § 3

(a) For the direct sum of a family $(E_\lambda)$ of $A$-modules to be faithfully flat, it is sufficient that each of the $E_\lambda$ be flat and that at least one of them be faithfully flat.

(b) Deduce from (a) that, if $A$ is a simple ring, every non-empty $A$-module is faithfully flat. Is the result true for semisimple rings?