Stone Lattices. II. Structure Theorems

Abstract

Using the triple associated with a Stone algebra L, as introduced in the first part of this paper (1), we will investigate certain problems concerning the structure of a Stone lattice.The following topics will be discussed: prime ideals, topological representation, completeness, relative Stone lattices, and the reduced triple.It is assumed that the reader is familiar with §§ 2–4 of (1). For the sake of convenience, we will write L= 〈C, D, ϕ〉 to indicate that 〈C, D, ϕ〉 is the triple associated with L, and whenever convenient we will write the elements of L as ordered pairs 〈x, a〉, as it is given in (1, § 4, the Construction Theorem).