Coproducts of bounded distributive lattices: cancellation. (Q1771846)

In the paper the following problem from the 1981 Banff Conference on ordered sets is solved: What is the largest class \(\mathcal L\) of finite distributive lattices such that, for every non-trivial Boolean lattice \(B\) and every \(L\in \mathcal L\), the equality of coproducts \(B\ast L = B\ast L'\) implies \(L=L'\)? \(\mathcal L\) is shown to be the class of all finite rigid distributive lattices.