Let $A_n$ denote the Weyl algebra - the algebra of partial differential operators in $n$ variables with polynomial coefficients.
In papers I've read the following definition:
A left ideal $I$ of $A_n$ is called zero-dimensional, if $\dim_{K(x_1,...,x_n)} A_n/I \lt \infty$.
My question: How can we view $A_n/I$ or generally $A_n$ as $K(x_1,...,x_n)$-vector space?