  This paper compares skew-linear and multilinear matroid representations.
These are matroids that are representable over division rings and (roughly
speaking) invertible matrices, respectively. The main tool is the von Staudt
construction, by which we translate our problems to algebra. After giving an
exposition of a simple variant of the von Staudt construction we present the
following results:
  $\bullet$ Undecidability of several matroid representation problems over
division rings.
  $\bullet$ An example of a matroid with an infinite multilinear characteristic
set, but which is not multilinear in characteristic $0$.
  $\bullet$ An example of a skew-linear matroid that is not multilinear.
