## Over a commutative ring, the tensor product of two flat modules is flat

Let $R$ be a commutative ring and let $M$ and $N$ be $R$-modules. Show that if $M$ and $N$ are flat over $R$, then $M \otimes_R N$ is flat over $R$.

This is a special case of the previous exercise, since both $M$ and $N$ can naturally be considered $(R,R)$-bimodules.