Ideal Extensions of Topological Semigroups

Jr., Francis T. Christoph

Canadian journal of mathematics, Tome 22 (1970) no. 6, pp. 1168-1175

Résumé

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.

Détail

DOI : 10.4153/CJM-1970-134-0

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