Finiteness of a 3-Generated Lattice with Seminormal and Coseminormal Elements Among Generators

Resumo

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.