Hostname: page-component-77c89778f8-vpsfw Total loading time: 0 Render date: 2024-07-16T18:11:37.005Z Has data issue: false hasContentIssue false
  • English
  • Français

A construction of a compact right topological semigroup

Published online by Cambridge University Press:  24 October 2008

Ahmed El-Mabhouh
Ahmed El-Mabhouh
Affiliation:
Department of Pure Mathematics, The University, Sheffield S3 7RH, England
Get access Rights & Permissions [Opens in a new window]

Extract

It is well-known that the structure of βℕ, the Stone—Čech compactification of the discrete semigroup (ℕ, +), is very complex. For example, it has 2c minimal left ideals and 2c minimal right ideals, its minimal ideal contains 2c copies of the free group on 2c generators, see [5], and Lisan[8] proved the existence of 2c copies of the same group outside the closure of the minimal ideal.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 116 , Issue 2 , September 1994 , pp. 317 - 323
Copyright
Copyright © Cambridge Philosophical Society 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Baker, J. W. and Milnes, P.. The ideal structure of the Stone—Čech compactification of a group. Math. Proc. Cambridge Philos. Soc. 82 (1977), 401–409.CrossRefGoogle Scholar
[2]Berglund, J. F., Junghenn, H. D. and Milnes, P.. Analysis on semigroups. (Wiley, 1989).Google Scholar
[3]Helmer, D. and Išik, N.. Construction of right topological compactifications for discrete versions of subsemigroups of compact groups. Semigroup Forum 39 (1989), 65–73.CrossRefGoogle Scholar
[4]Hindman, N.. The ideal structure of the space of κ-uniform ultrafilters on a discrete semigroup. Rocky Mountain J. Math. 16 (1986), 685–701.CrossRefGoogle Scholar
[5]Hindman, N. and Pym, J. S.. Free groups and semigroups in βℕ. Semigroup Forum 30 (1984), 177–193.CrossRefGoogle Scholar
[6]Hippisley-Cox, S. D.. Finite point compactifications of (ℕ, +). Semigroup Forum 44 (1992), 388–392.CrossRefGoogle Scholar
[7]Lau, A. T., Milnes, P. and Pym, J. S.. Compactifications of locally compact groups and closed subgroups. Trans. American Math. Soc. 329 (1992), 97–115.CrossRefGoogle Scholar
[8]Lisan, A. T.. Free groups in βℕ which miss the minimal ideal. Semigroup Forum 37 (1988), 233–239.CrossRefGoogle Scholar
[9]Papazyan, T.. Oids, finite sums and the structure of the Stone—Čech compactification of a discrete semigroup. Semigroup Forum 42 (1991), 265–277.CrossRefGoogle Scholar
[10]Pym, J. S.. A topological construction in the theory of semigroup compactifications. J. Nigerian Math. Soc. 2 (1983), 39–53.Google Scholar
[11]Pym, J. S.. A construction of compact right topological semigroups from compact groups. Semigroup Forum 35 (1987), 207–225.CrossRefGoogle Scholar
[12]Pym, J. S.. Semigroup structure in Stone—Čech compactifications. J. London Math. Soc. 36 (1988), 421–428.Google Scholar