Let $A_{n}$ be the $n$th Weyl algebra over a field, with generators $x_{1}, \ldots, x_{n}, y_{1}, \ldots, y_{n}$. Why is the Krull dimension of the rigth $A_{n}$-module $A_{n}/x_{1}A_{n}$ equal to $n-1$? I've been reading Stafford's paper on non-holonomic modules but I got stuck at this point. Meybe this is easy but I don't know much about Krull dimension.
I know it must be less than or equal to $n-1$ but I couldn't find the lower bound.