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Stone Lattices. II. Structure Theorems

Published online by Cambridge University Press:  20 November 2018

C. C. Chen  and
G. Grätzer
C. C. Chen
Affiliation:
Queen's University, Kingston, Ontario
G. Grätzer
Affiliation:
Nanyang University, Singapore, Malaysia University of Manitoba, Winnipeg, Manitoba
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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).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 895 - 903
Copyright
Copyright © Canadian Mathematical Society 1969

References

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