It is well-know that the tensor product of two finitely generated modules over a given ring $R$ is finitely generated. Now my question is
Let $M$ and $N$ be $R$-modules where $R$ is a commutative ring. If $N$ is a FG module and we know that $M$ is not a FG module. Then what happens for the tensor product of $M$ and $N$ over $R$. Can we say that it is not FG or it may be FG. I am interested in the later case.