Weak bases in modular lattices
Zsolt Lengvárszky · Czechoslovak Mathematical Journal · 1990
A subset H of a lattice Lis called weakly independent iff for all h, h 1 , ..In a lattice of finite length any chain is aweakly independent subset and any maximal chain is a weak basis.In a finite distributive lattice any set ofjoin-irreducible elements is weakly independent and the set of all join-irreducibles is a weak basis.Thus the following theorem which was proved in [1] generalizes the well-known fact that in a finite distributive lattice the number of elements in a maximal chain equals the number ofjoin-irreducible elements.