In the book "Rings and Categories of Modules" by Anderson & Fuller, this problem is given: If $V^A$, i.e. the direct product of the module $V$ by the index set $A$, is flat for all sets $A$, then $(V^{(B)})^A$ is flat for all sets $A$and $B$. My try: the module $V$is itself flat by adopting a one-element set $A$ in the hypothesis. Hence, any direct sum $V^{(B)}$ is also flat (for all sets $B$). Also, by Exercise 4.2 of Lam's book "Exercises in Modules and Rings", if every finitely generated submodule of a module $P$ is contained in a flat submodule of $P$, then $P$ itself is a flat module. Any help would be appreciated.