$M \bigotimes_R (\Pi_{i\in I} B_i) \ncong \Pi_{i \in I} (M \bigotimes B_i)$

52 Views Asked by At

let M and Bi be R-MODULE for all i in I Show that $M \bigotimes_R (\Pi_{i\in I} B_i) \ncong \Pi_{i \in I} (M \bigotimes B_i)$ Take $R=\mathbb{Z}$, $M=\mathbb{Q}$ and $B_n =\frac{\mathbb{Z}}{P^n \mathbb{Z}}$ , n > 0