Rosenbrock's Theorem characterizes Prüfer domains

Under coprimality assumptions on certain submatrices, Rosenbrock's Theorem relates the Smith form of a matrix $P$ over an elementary divisor domain $\mathcal{R}$ to the Smith-McMillan form of a matrix $G$ over the field of fractions of $\mathcal{R}$, where $G$ is a Schur complement in $P$. If $\math