ACTA issues

Notes on CD-independent subsets

Eszter K. Horváth, Sándor Radeleczki

Acta Sci. Math. (Szeged) 78:1-2(2012), 3-24

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.)