On projective embeddings of partial planes and rank-three matroids

Any finite partial plane f, and thus any finite linear space and any (simple) rank-three matroid, can be embedded into a translation plane. It even turns out, that f is embeddable into a projective plane of Lenz class V, and that the characteristic of this plane can be chosen arbitrarily. In particular, any rank three matroid is realizable over a (not necessarily associative) division algebra.