Minimal extensions of distributive bounded lattices
M. E. Adams, Jürg Schmid · 2008
Dedicated to the memory of Ph. Dwinger Abstract. There is a considerable literature on (proper) maximal sublat-tices of distributive bounded lattices. In this note, we consider the dual concept of when L ′ is a minimal extension of L, that is L is a (proper) maximal sublattice of L′. Minimal extensions occur in one of two ways, so-called removing a cover or splitting a point. The removal of covers is characterised and special points that can always be split are identified. For infinite L, there are at least |L | minimal extensions obtained by splitting spe-cial points, examples are given to show that there need be no other minimal extensions. 1.