ON PARTIALLY ORDERED SETS REPRESENTABLE OVER CLASSES OF DISTRIBUTIVE LATTICES

Abstract

In this thesis, we shall characterize those posets representable over various classes of distributive lattices. In Chapter One , we give the basic notion of lattices and some useful properties of distributive lattices. A method of construction of the finite distributive lattice, whose poset of prime ideals is a given poset, is given in Chapter Two . In Chapter Three , we study the representations of some classes of finite distributive lattices, namely, chains, boolean 'lattices, ston^ lattices and planar and distributive lattices. The representations of the class of relatively complemented distributive lattices ??he class of distri— butive lattices generated by meet-irreducible elements, the class of free distributive lattices on \x\ free generators, and finally ? he class of general distributive lattices are given in Chapter Four .