Let $M_1$ and $M_2$ be Cohen-Macaulay modules over a ring $R$. When is $M_1 \otimes_R M_2$ a Cohen-Macaulay module over $R$?
That is the finite question I have. Motivation: I know that when $M$ is a Cohen-Macaulay module then $M \otimes_R R[x_1,...,x_n]$ is Cohen-Macaulay. Power series over Cohen-Macaulay modules are also Cohen-Macaulay, if the proof I did just now is correct. These are both examples of positive answers to my question.