1. CMB 2011 (vol 54 pp. 277)
 Farley, Jonathan David

Maximal Sublattices of Finite Distributive Lattices. III: A Conjecture from the 1984 Banff Conference on Graphs and Order
Let $L$ be a finite distributive lattice. Let
$\operatorname{Sub}_0(L)$ be the lattice
$$
\{S\mid S\text{ is a sublattice of }L\}\cup\{\emptyset\}
$$
and let $\ell_*[\operatorname{Sub}_0(L)]$ be the length of the shortest maximal chain in $\operatorname{Sub}_0(L)$. It is proved that if $K$ and $L$ are nontrivial finite distributive lattices, then
$$
\ell_*[\operatorname{Sub}_0(K\times L)]=\ell_*[\operatorname{Sub}_0(K)]+\ell_*[\operatorname{Sub}_0(L)].
$$
A conjecture from the 1984 Banff Conference on Graphs and Order is thus proved.
Keywords:(distributive) lattice, maximal sublattice, (partially) ordered set Categories:06D05, 06D50, 06A07 

2. CMB 1997 (vol 40 pp. 39)
 Zhao, Dongsheng

On projective $Z$frames
This paper deals with the projective objects in the category of all
$Z$frames, where the latter is a common generalization of
different types of frames. The main result obtained here is that a
$Z$frame is ${\bf E}$projective if and only if it is stably
$Z$continuous, for a naturally arising collection ${\bf E}$ of morphisms.
Categories:06D05, 54D10, 18D15 
