|
Abstract. It is proved in [CHS] that any two CD-bases in a finite distributive lattice have the same number of elements. We investigate CD-bases in posets, semilattices and lattices. It is shown that their CD-bases can be characterized as maximal chains in a related poset or lattice. We point out two known lattice classes characterized by some ``$0$-conditions" whose CD-bases satisfy the mentioned property.
AMS Subject Classification
(1991): 06A06, 06B99
Keyword(s):
CD-base,
disjoint system,
distributive pair,
$0$-modular lattice
Received September 18, 2010, and in final form March 25, 2011. (Registered under 67/2010.)
|