Let $A$ and $B$ be $\mathbb{C}$-algebras. Suppose that $M$ and $N$ are respectively simple $A$ and $B$ modules.

We can regard $M\otimes_{\mathbb C}N$ as $A\otimes_{\mathbb C} B$-modules in natural way.

${\bf My\ Question:}$ Is $M\otimes_{\mathbb{C}} N$ still a simple $A\otimes_{\mathbb C} B$-module? What conditions on $A$, $B$, $M$ and $N$ will make this result true? Thanks very much in advance!