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Lattices generated by modular element

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We prove that the lattice generated by three modular elements is modular. For every n > 3 we construct a nonmodular lattice L generated by n elements each of which is modular in L.

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Correspondence to M. P. Shushpanov.

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Original Russian Text © M.P. Shushpanov, 2015, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, No. 12, pp. 84–86.

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Shushpanov, M.P. Lattices generated by modular element. Russ Math. 59, 73–75 (2015).

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