Hostname: page-component-848d4c4894-r5zm4 Total loading time: 0 Render date: 2024-06-25T20:41:30.613Z Has data issue: false hasContentIssue false

Some properties of the lattice of subalgebras of a Boolean algebra

Published online by Cambridge University Press:  17 April 2009

Ivo Düntsch
Affiliation:
Department of Mathematics, University of Brunei Darussalam, Bandar Sen Begawan, Brunei.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We investigate the structure of the lattice of subalgebras of an infinite Boolean algebra; in particular, we make a contribution to the question as to when such a lattice is simple.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Birkhoff, G., “Lattice Theory”, (American Mathematical Society, Providence, 1948).Google Scholar
[2]van Douwen, E., Monk, D., Rubin, M., “Some questions about Boolean algebras”, Algebra Universalis 11 (1980), 220243.CrossRefGoogle Scholar
[3]Grätzer, G., “General Lattice Theory”, (Academic Press, New York, Basel, 1978).CrossRefGoogle Scholar
[4]Rubin, M., “A Boolean algebra with few subalgebras, interval algebras, and retractiveness”, Trans. Amer. Math. Soc. 278 (1983), 6589.CrossRefGoogle Scholar
[5]Sachs, D., “The lattice of subalgebras of a Boolean algebra”, Canad. Math. J. 29 (1962), 451460.CrossRefGoogle Scholar
[6]Todorčević, S., “A remark on the lattice of all subalgebras of a Boolean algebra”, unpublished.Google Scholar