On projective embeddings of partial planes and rank-three matroids

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