CD-independent subsets in distributive lattices

摘要

The main result says that any two CD-bases of a finite distributive lattice L havethe same number of elements. It is also shown that distributivity cannot be replaced bya weaker lattice identity. However, weaker assumptions on L are still relevant: semimod-ularity implies that no CD-basis can have fewer elements than a maximal chain, whilelower semimodularity yields that each maximal chain together with all atoms forms aCD-basis.