Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-24T21:57:21.599Z Has data issue: false hasContentIssue false

Lattices, complements and tight Riesz orders

Published online by Cambridge University Press:  09 April 2009

Neil Cameron
Affiliation:
Department of Mathematics, Monash University, Clayton Victoria, 3168, Australia
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.

It is proved that there exists no compatible tight Riesz order on a complemented modular lattice. An example is provided of a complemented lattice with a compatible tight Riesz order.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1976

References

Cameron, Neil and Miller, J. B., ‘Topology and axioms of interpolation in partially ordered spaces’, J. fur die reine u. angewandte Math. (to appear).Google Scholar
Loy, R. J. and Miller, J. B. (1972), ‘Tight Riesz Groups’, J. Austral. Math. Soc. 13, 224240.CrossRefGoogle Scholar
Reilly, N. R. (1973), ‘Compatible tight Riesz orders and prime subgroups’, Glasgow Math. J. 14, 146160.CrossRefGoogle Scholar
Wirth, A. (1973), ‘Compatible tight Riesz orders’, J. Austral. Math. Soc. 15, 105–11.CrossRefGoogle Scholar