No CrossRef data available.
Article contents
Compatible tight Riesz orders on groups of integer-valued functions
Published online by Cambridge University Press: 17 April 2009
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.
A construction due to Reilly is extended to show that there is a correspondence between compatible tight Riesz orders on ZX and non-principal filters on X. The maximal compatible tight Riesz orders are in one-to-one correspondence with non-principal ultra-filters, and are dual prime subsets of the positive set of ZX. Conversely every dual prime algebraic Riesz order is maximal.
- Type
- Research Article
- Information
- Copyright
- Copyright © Australian Mathematical Society 1975
References
[1]Bell, J.L. and Slomson, A.B., Models and ultraproducts: an introduction (North-Holland, Amsterdam, London, 1969).Google Scholar
[2]Gillman, Leonard and Jerison, Meyer, Rings of continuous functions (Van Nostrand, Princeton, New Jersey; Toronto; London; New York; 1960).Google Scholar
[3]Lane, S. Mac, Categories for the working mathematician (Graduate Texts in Mathematics, 5. Springer-Verlag, New York, Heidelberg, Berlin, 1971).Google Scholar
[4]Reilly, N.R., “Compatible tight Riesz orders and prime subgroups”, Glasgow Math. J. 14 (1973), 145–160.Google Scholar
[5]Wirth, Andrew, “Compatible tight Riesz orders”, J. Austral. Math. Soc. 15 (1973), 105–111.CrossRefGoogle Scholar
You have
Access