Geodesic
Finiteness of a $3$-generated lattice with seminormal and coseminormal elements among generators
Algebra i logika, Tome 57 (2018) no. 3, pp. 362-376

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It is known that a modular $3$-generated lattice is always finite and contains at most 28 elements. Lattices generated by three elements with certain modularity properties may no longer be modular but nevertheless remain finite. It is shown that a $3$-generated lattice among generating elements of which one is seminormal and another is coseminormal is finite and contains at most 45 elements. This estimate is stated to be sharp.
Keywords: left-modular element, right-modular element, seminormal element, defining relation. 
@article{AL_2018_57_3_a6,
     author = {M. P. Shushpanov},
     title = {Finiteness of a~$3$-generated lattice with seminormal and coseminormal elements among generators},
     journal = {Algebra i logika},
     pages = {362--376},
     publisher = {mathdoc},
     volume = {57},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2018_57_3_a6/}
}
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M. P. Shushpanov. Finiteness of a $3$-generated lattice with seminormal and coseminormal elements among generators. Algebra i logika, Tome 57 (2018) no. 3, pp. 362-376. http://geodesic.mathdoc.fr/item/AL_2018_57_3_a6/