Abstract:The rank of a point-line geometry Γ is usually defined as the generating rank of Γ, namely the minimal cardinality of a generating set. However, when the subspace lattice of Γ satisfies the Exchange Property we can also try a different definition: consider all chains of subspaces of Γ and take the least upper bound of their lengths as the rank of Γ. If Γ is finitely generated then these two definitions yield the same number. On the other hand, as we shall show in this paper, if infinitely many points are neede… Show more
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