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Representation of Boolean hypolattices

Published online by Cambridge University Press:  17 April 2009

John Boris Miller
John Boris Miller
Affiliation:
Department of Mathematics, Monash University, Clayton, Victoria 3168.
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Abstract

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The principal result is a representation theorem for relatively-distributive, relatively complemented hypolattices with zero, generalizing the Stone representation theorem for a Boolean lattice. It uses the small product of a family of Boolean lattices which are maximal sublattices of the hypolattice. The paper also characterizes the maximal sublattices when the hypolattice is coherent; and it gives several examples of hypolattices, including hypolattices of subgroups and of ideals by direct sum, and examples from relative convexity, relative closure, and cofinality.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 24 , Issue 3 , December 1981 , pp. 389 - 404
Copyright
Copyright © Australian Mathematical Society 1981

References

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