The statement of the Weierstrass Preparation Theorem is as follows:
Let $f = \sum_{i=0}^\infty a_iX^i \in K[[X]]$ for some field K where $a_h \neq 0$ and for every $n < h$, $a_n = 0$. Then the elements 1,$\bar x$, ... , $\bar x^{h-1}$ form a basis in $K[[X]]/(f)$ over $K$.
My question is how does one generalize and prove this statement for a ring of formal power series in n variables?