Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-16T16:16:39.486Z Has data issue: false hasContentIssue false
  • English
  • Français

The lateral completion of a completely distributive lattice-ordered group (revisited)

Part of: Ordered structures

Published online by Cambridge University Press:  09 April 2009

Gary Davis  and
Stephen H. McCleary
Gary Davis
Affiliation:
La Trobe University, Bundoora, Victoria, Australia
Stephen H. McCleary
Affiliation:
University of Georgia, Athens, Georgia, U.S.A.
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.

The lateral completion of a completely distributive lattice-ordered permutation group is investigated via various completions, obtained by adjoining permutations which match some elements of the given group in various ways. This makes known results on the lateral completion of a completely distributive lattice-ordered group both transparent and easy.

MSC classification

Secondary: 06F15: Ordered groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 31 , Issue 1 , June 1981 , pp. 114 - 128
Copyright
Copyright © Australian Mathematical Society 1981

References

[1] Ball, R., ‘Topological lattice ordered groups’, to appear.Google Scholar
[2] Ball, R., ‘Convergence and Cauchy structures on lattice ordered groups’, to appear.Google Scholar
[3] Bernau, S. J., ‘The lateral completion of an arbitrary lattice group’, J. Austral. Math. Soc. Ser. A 19 (1975), 263–289.CrossRefGoogle Scholar
[4] Bernau, S. J., ‘Varieties of lattice groups are closed under L-completion’, Symposia Math. 21 (1977), 349–355.Google Scholar
[5] 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.CrossRefGoogle Scholar
[6] Byrd, R. D., ‘Complete distributivity in lattice-ordered groups’, Pacific J. Math. 20 (1967), 423–432.CrossRefGoogle Scholar
[7] Byrd, R. D. and Lloyd, J. T., ‘Closed subgroups and complete distributivity in lattice-ordered groups’, Math. Zeit 101 (1967), 123–130.CrossRefGoogle Scholar
[8] Byrd, R. D., A note on lateral completions in lattice-ordered groups, J. London Math. Soc. (2) (1969), 358–362.CrossRefGoogle Scholar
[9] Conard, P., ‘The lateral completion of a lattice-ordered group’, Proc. London Math. Soc. (3) 19 (1969), 444–480.CrossRefGoogle Scholar
[10] Glass, A. M. W., Ordered permutation groups (Bowling Green State University, Bowling Green, Ohio, 1976).Google Scholar
[11] Glass, A. M. W., Holland, W. C. and McClearly, S. H., ‘a*-closures of completely distributive lattice-ordered groups’, Pacific J. Math. 59 (1975), 43–67.CrossRefGoogle Scholar
[12] Holland, W. C. and McCleary, S. H., ‘Wreath products of ordered permutation groups’, Pacific J. Math. 31 (1969), 703–716.CrossRefGoogle Scholar
[13] McClearly, S. H., ‘The closed prime subgroups of certain ordered permutation groups’, Pacific J. Math. 31 (1969), 745–753.CrossRefGoogle Scholar
[14] McClearly, S. H., ‘O-primitive ordered permutation groups’, Pacific J. Math. 40 (1972), 349–372.CrossRefGoogle Scholar
[15] McClearly, S. H., ‘Closed subgroups of lattice-ordered permutation groups’, Trans. Amer. Math. Soc. 173 (1972), 303–314.CrossRefGoogle Scholar
[16] McClearly, S. H., ‘The structure of intransitive ordered permutation groups, Algebra Universalis 6 (1976), 229–255.CrossRefGoogle Scholar