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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
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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

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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