On the relation of a distributive lattice to its lattice of ideals
Herbert S. Gaskill · Bulletin of the Australian Mathematical Society · 1972
In this note we examine the relationship of a distributive lattice to its lattice of ideals. Our main result is that a distributive lattice and its lattice of ideals share exactly the same collection of finite sublattices. In addition we give a related result characterizing those finite distributive lattices L which can be embedded in a lattice L′ whenever they can be embedded in its lattice of ideals T(L′).