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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 non-trivial 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 setCategories: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