Abstract:A basic property in a modular lattice is that any two flags generate a distributive sublattice. It is shown , Herscovic 1998 that two flags in a semimodular lattice no longer generate such a good sublattice, whereas shortest galleries connecting them form a relatively good join-sublattice. In this note, we sharpen this investigation to establish an analogue of the two-flag generation theorem for a semimodular lattice. We consider the notion of a modular convex subset, which is a subset closed under the join an… Show more
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