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An inverse limit representation for complete Boolean algebras

Published online by Cambridge University Press:  18 May 2009

R. Beazer
R. Beazer
Affiliation:
University of Glasgow, Glasgow, G12 8QQ
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There are two well-known methods to build up algebras from given algebras, the direct and inverse limits, and a systematic account of these constructions may be found in [2]. It is known that every algebra can be represented as a direct limit of finitely generated algebras although in some cases the representation is trivial. Furthermore, Haimo [3] has established a certain inverse limit representation for the class of all infinite Boolean algebras which generalises, in actual fact, to the class of all infinite lattices with 1. The purpose of this note is to exhibit a certain nontrivial inverse limit representation which is peculiar to the class of infinite, complete Boolean algebras.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 13 , Issue 2 , September 1972 , pp. 164 - 166
Copyright
Copyright © Glasgow Mathematical Journal Trust 1972

References

REFERENCES

1.Birkhoff, G., Lattice Theory, Amer. Math. Soc. Colloqium Publications Vol. 25, 3rd edition (Providence, R. I., 1967).Google Scholar
2.Grätzer, G., Universal Algebra (New York, 1968).Google Scholar
3.Haimo, F., Some limits of Boolean algebras. Proc. Amer. Math. Soc. 2 (1951), 566–576.CrossRefGoogle Scholar