Finitely generated lattices with completely modular elements among generators
Algebra i logika, Tome 52 (2013) no. 6, pp. 657-666

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We look at the concept of a completely modular element of a lattice, which is the modular analog of the well-known concept of a neutral element of a lattice. It is proved that a lattice is modular if it is generated by three elements of which two are completely modular. Also it is shown that a lattice generated by $n$, $n>3$, completely modular elements must not necessarily be modular.
Keywords: modular lattices, free lattices, modular elements.
@article{AL_2013_52_6_a0,
     author = {A. G. Gein and M. P. Shushpanov},
     title = {Finitely generated lattices with completely modular elements among generators},
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     publisher = {mathdoc},
     volume = {52},
     number = {6},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2013_52_6_a0/}
}
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A. G. Gein; M. P. Shushpanov. Finitely generated lattices with completely modular elements among generators. Algebra i logika, Tome 52 (2013) no. 6, pp. 657-666. http://geodesic.mathdoc.fr/item/AL_2013_52_6_a0/