Let α be an infinite cardinal. Let Tα be the class of all lattices which are conditionally α-complete and infinitely distributive. We denote by T'α the class of all lattices X such that X is infinitely distributive, α-complete and has the least element. In this paper we deal with direct factors of lattices belonging to T α - As an application, we prove a result of Cantor-Bernstein type for lattices belonging to the class T'α.
Let D be the system of all distributive lattices and let D0 be the system of all L ∈ D such that L possesses the least element. Further, let D1 be the system of all infinitely distributive lattices belonging to D0. In the present paper we investigate the radical classes of the systems D, D0 and D1.