Maximal sublattices and Frattini sublattices of bounded lattices
M. E. Adams, Ralph S. Freese, James B. Nation, Jürg Schmid · Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics · 1997
Abstract We investigate the number and size of the maximal sublattices of a finite lattice. For any positive integerk, there is a finite lattice L with more that ]L]ksublattices. On the other hand, there are arbitrary large finite lattices which contain a maximal sublattice with only 14 elements. It is shown that every bounded lattice is isomorphic to the Frattini sublattice (the intersection of all maximal sublattices) of a finite bounded lattice.