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A class of projective Stone algebras

Published online by Cambridge University Press:  17 April 2009

Ivo Düntsch
Ivo Düntsch
Affiliation:
Freie Universität, FB 10, Garystr. 21, 1000 Berlin 33, West Germany.
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Abstract

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We prove that a regular double Stone algebra is protective in the category of Stone algebras if and only if its centre is a projective Boolean algebra and its dense set is countably generated as a filter. It follows that every countable regular double Stone algebra is projective as a Stone algebra.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 24 , Issue 1 , August 1981 , pp. 133 - 147
Copyright
Copyright © Australian Mathematical Society 1981

References

[1]Balbes, R. and Grätzer, G., “Injective and projective Stone algebras”, Duke Math. J. 38 (1971), 339–347.Google Scholar
[2]Balbes, Raymond and Horn, Alfred, “Stone lattices” Duke Math. J. 37 (1970), 537–545.Google Scholar
[3]Chen, C.C. and Grätzer, G., “Stone lattices. I: Construction theorems”, Canad. J. Math. 21 (1969), 884–894.CrossRefGoogle Scholar
[4]Düntsch, Ivo, “Projectivity, prime ideals and chain conditions of Stone algebras”, Algebra Universalis (to appear).Google Scholar
[5]Grätzer, George, Lattice theory. First concepts and distributive lattices (Freeman, San Francisco, California, 1971).Google Scholar
[6]Katrin˘ák, T., “Die freien Stoneschen Verbände und ihre Tripelcharakterisierung”, Acta Math. Acad. Sci. Hungar. 23 (1972), 315–326.CrossRefGoogle Scholar
[7]Katrin˘ák, Tibor, “Construction of regular double p-algebras”, Bull. Soc. Roy. Sci. Liège 43 (1974), 283–290.Google Scholar
[8]Varlet, J., “A regular variety of type (2, 2, 1, 1, 0, 0,)”, Algebra Universalis 2 (1972), 218–223.CrossRefGoogle Scholar