No CrossRef data available.
Article contents
Representation of Boolean hypolattices
Published online by Cambridge University Press: 17 April 2009
Abstract
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