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Certain Finitely Generated Compact Zero Dimensional Semigroups

Published online by Cambridge University Press:  09 April 2009

R. P. Hunter
Affiliation:
Department of MathematicsPennsylvania State UniversityUniversity Park, Pennsylvania 16802, U.S.A.
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Abstract

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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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1988

References

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