Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-08T07:28:34.688Z Has data issue: false hasContentIssue false
  • English
  • Français

The Completion of an Abelian l-Group

Published online by Cambridge University Press:  20 November 2018

G. Otis Kenny
G. Otis Kenny*
Affiliation:
University of Kansas, Lawrence, Kansas
Rights & Permissions [Opens in a new window]

Extract

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 directed partially ordered abelian group (G, ≦ ) is a tight Riesz group if for a1, a2, b1, b2 ∈ G with ai < bj, i, j = 1,2, there is an x ∈ G with ai < x < bj, i, j = 1, 2. The open interval topology on G is the topology having as a base the set of all open intervals (a, b) = {x ∈ G|a < x < b}. For any x ∈ G, a neighborhood base at x is the set of all open intervals (x — a, x + a) = x + ( — a, a) for a > 0.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 5 , 01 October 1975 , pp. 980 - 985
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Banaschewski, B., Uber die Vervollstdndigung geordneter Gruppen, Math. Nachr. 16 (1957), 51–71.Google Scholar
2. Bleier, R. and Conrad, P., The lattice of closed ideals and a*-extensions of an abelian l-group, Pacific J. Math. 47 (1973), 329–340.Google Scholar
3. Everett, C. J., Lattice modules, Duke Math. J. 11 (1944), 109–119.Google Scholar
4. Bourbaki, N., General topology, Part /, Elements of Mathematics Series (Addison-Wesley, Reading, Mass., 1966).Google Scholar
5. Holland, C., Extensions of ordered groups and sequence completions, Trans. Amer. Math. Soc. 107 (1963), 71–82.Google Scholar
6. Loy, R. J. and Miller, J. B., Tight Riesz groups, J. Austral. Math. Soc. 13 (1972), 224–240.Google Scholar
7. Reilly, N. R., Compatible tight Riesz orders and prime subgroups, Glasgow Math. J. 14 (1973), 145–160.Google Scholar
8. Wirth, A., Compatible tight Riesz orders, J. Austral. Math. Soc. 15 (1973), 105–111.Google Scholar