Finite distributive lattices are congruence lattices of almost-geometric lattices

摘要

A semimodular lattice L of finite length will be called an almost-geometric lattice if the order J(L) of its nonzero join-irreducible elements is a cardinal sum of at most two-element chains. We prove that each finite distributive lattice is isomorphic to the lattice of congruences of a finite almost-geometric lattice.