Certain Finitely Generated Compact Zero Dimensional Semigroups
- 9 April 1988
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
- Vol. 44 (2) , 265-270
- https://doi.org/10.1017/s1446788700029852
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. 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.Keywords
This publication has 2 references indexed in Scilit:
- Some Results on Stability in SemigroupsTransactions of the American Mathematical Society, 1965
- Theorems on Compact Totally Disconnected Semigroups and LatticesProceedings of the American Mathematical Society, 1957