The Central Decomposition of FD01(n)

The paper presents a method of composing finite distributive lattices from smaller pieces and applies this to construct the finitely generated free distributive lattices from appropriate Boolean parts.

Compatible Algebras with Straightening Laws on Distributive Lattices

We characterize the finite distributive lattices on which there exists a unique compatible algebra with straightening laws.

On (finite) distributive lattices with antitone involutions

Finite distributive lattices with antitone involutions (= basic algebras) are studied; it is proved that their underlying lattices are isomorphic to direct products of finite chains, and hence finite distributive basic algebras can be constructed by “perturbing” finite MV-algebras, and moreover, under certain natural conditions, they even coincide with finite MV-algebras.

On Subdirect Decompositions of Finite Distributive Lattices

Subdirect decomposition of algebra is one of its quite general and important constructions. In this paper, some subdirect decompositions (including subdirect irreducible decompositions) of finite distributive lattices and finite chains are studied, and some general results are obtained.