Coproducts of Bounded Distributive Lattices: Cancellation (A Banff Conference Problem)

Jonathan David Farley

Let $L*M$ denote the coproduct of the bounded distributive lattices $L$ and $M$. At the 1981 Banff Conference on Ordered Sets, the following question was posed: What is the largest class $\mathcal L$ of finite distributive lattices such that, for every non-trivial Boolean lattice $B$ and every $L\in\mathcal L$, $B*L=B*L'$ implies $L=L'$?

In this note, the problem is solved.