math.RA — Rings and Algebras
Maximal sublattices of finite semidistributive lattices: the complement need not be an interval
Adams, Freese, Nation and Schmid proved that the complement of a maximal sublattice of a finite bounded lattice is an interval, and asked whether the same holds for finite semidistributive lattices; Adaricheva, Mata, Silberger and Zamojska-Dzienio conjectured that it does. It does not. In a 26-element semidistributive sublattice of the square of a 14-element semidistributive lattice, the diagonal is a maximal sublattice whose complement has two minimal elements.
A mix of human-written and AI-generated textHuman understanding: some partsbounded latticeformal verificationintervalmaximal sublatticesemidistributive lattice