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Lattices, complements and tight Riesz orders

Published online by Cambridge University Press:  09 April 2009

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

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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
Information
Journal of the Australian Mathematical Society , Volume 21 , Issue 3 , May 1976 , pp. 368 - 370
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, 224–240.CrossRefGoogle Scholar
Reilly, N. R. (1973), ‘Compatible tight Riesz orders and prime subgroups’, Glasgow Math. J. 14, 146–160.CrossRefGoogle Scholar
Wirth, A. (1973), ‘Compatible tight Riesz orders’, J. Austral. Math. Soc. 15, 105–11.CrossRefGoogle Scholar