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Ideal Extensions of Topological Semigroups

Published online by Cambridge University Press:  20 November 2018

Francis T. Christoph Jr.
Francis T. Christoph Jr.*
Affiliation:
Temple University, Philadelphia, Pennsylvania
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In the study of compact semigroups the constructive method rather than the representational method is usually the better plan of attack. As it was pointed out by Hofmann and Mostert in the introduction to their book [10] this method is more productive than searching for a representation theory. Hofmann and Mostert described a constructive method called the Hormos and showed that any irreducible compact semigroup is obtained by the Hormos construction. Many of the important examples of irreducible semigroups which motivated their work were obtained by Hunter [11; 12; 13; 14].

In this paper, we apply the constructive method of ideal extensions [5] in algebraic semigroups to topological semigroups which are not necessarily compact. Many of Hunter's examples and examples of the Hormos technique can also be obtained by our method of topological ideal extensions. The topological ideal extension method, however, is, in general, a different type of construction technique.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 6 , 01 December 1970 , pp. 1168 - 1175
Copyright
Copyright © Canadian Mathematical Society 1970

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