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Stone Lattices. I: Construction 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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Stone lattices were (named and) first studied in 1957 (5). Since then, a great number of papers have been written on Stone lattices and a very satisfactory theory evolved. Despite the fact that all chains with 0, 1 as well as all Boolean algebras are Stone lattices, it turns out that many of the nice theorems on Boolean algebras have analogues, in fact, generalizations for Stone lattices. To give just two examples: the characterization of Boolean algebras in terms of prime ideals (Nachbin (6)) is generalized in (5) (see also (9)); Stone's representation theory (8) is generalized in (4); see also (2).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 884 - 894
Copyright
Copyright © Canadian Mathematical Society 1969

References

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