Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-28T08:14:03.805Z Has data issue: false hasContentIssue false
  • English
  • Français

Certain Finitely Generated Compact Zero Dimensional Semigroups

Part of: Topological and differentiable algebraic systems

Published online by Cambridge University Press:  09 April 2009

R. P. Hunter
R. P. Hunter
Affiliation:
Department of MathematicsPennsylvania State UniversityUniversity Park, Pennsylvania 16802, 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.

Consider a compact zero dimensional (profinite) monoid. While the group of units must be open, a regular D-class need not be open in the ideal it generates. This is the case if and only if the semigroup contains infinitely many copies of a certain semilattice composed of an increasing sequence of idempotents converging to an upper bound.

Using compactifications of free products, two generator compact monoids with these properties are constructed.

MSC classification

Secondary: 22A15: Structure of topological semigroups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 44 , Issue 2 , April 1988 , pp. 265 - 270
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Anderson, L. W., Hunter, R. P., and Koch, R. J., ‘Some results on stability in semigroups’, Trans. Amer. Math. Soc. 17 (1965), 521–529.CrossRefGoogle Scholar
[2]Anderson, L. W. and Hunter, R. P., ‘Homomorphisms having a given H-class as a single class’, J. Austral. Math. Soc. 15 (1973), 7–14.Google Scholar
[3]Clifford, A. H. and Preston, G. B., Algebraic theory of semigroups (Math. Surveys, no. 7, Amer. Math. Soc., 1961).CrossRefGoogle Scholar
[4]Hofmann, K. H. and Mostert, P. S., Elements of compact semigroups (Merrill, Columbus, Ohio, 1966).Google Scholar
[5]Hunter, R. P., ‘Some results on subgroups defined by the Bohr compactification’, Semigroup Forum 26 (1983), 125–137.CrossRefGoogle Scholar
[6]Numakura, K., ‘Theorems on compact totally disconnected semigroups and lattices’, Proc. Amer. Math. Soc. 8 (1957), 623–626.CrossRefGoogle Scholar