Stone Lattices. II. Structure Theorems

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).