J Austral Math Soc Ser A 44 pp265--270, 1988.

Certain Finitely Generated Compact Zero Dimensional Semigroups

R. P. Hunter

(Received 28 January 1986; revised 23 January 1987)

Abstract

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. Thi 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.

1980 AMS Subject Classification: 22A15

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Authors

R. P. Hunter: Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802, U.S.A.

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Last Modified: Wed Feb 19 10:27:48 2003