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Some remarks on modularity in prealgebraic and algebraic lattices. (English) Zbl 0764.06004

Summary: It is proved that every \(KI^*\)-lattice is modular. Further we shall give examples of an algebraic semimodular and lower semimodular lattice and of an atomistic \(QI\)-lattice which are not modular.

MSC:

06C05 Modular lattices, Desarguesian lattices
06C10 Semimodular lattices, geometric lattices
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