Direct product decompositions of infinitely distributive lattices
Ján Jakubík · Mathematica Bohemica · 2000
Let $\alpha$ be an infinite cardinal. Let $\Cal T_\alpha$ be the class of all lattices which are conditionally $\alpha$-complete and infinitely distributive. We denote by $\Cal{T}_\sigma'$ the class of all lattices $X$ such that $X$ is infinitely distributive, $\sigma$-complete and has the least element. In this paper we deal with direct factors of lattices belonging to $\Cal T_\alpha$. As an application, we prove a result of Cantor-Bernstein type for lattices belonging to the class $\Cal T_\sigma'$.