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A geometric lattice is the lattice of closed subsets of a closure operator on a set which is zero-closure, algebraic, atomistic and which has the so-called exchange property. There are many profound results about this type of lattices, the most recent one of which, due to Czédli and Schimdt (Adv Math 225:2455–2463, 2010), says that a lattice L of finite length is semimodular if and only if L has a...
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