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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Coverable semigroups


Author: A. Y. W. Lau
Journal: Proc. Amer. Math. Soc. 38 (1973), 661-664
MathSciNet review: 0310122
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Abstract: The concept of a semilattice having small semilattices has been studied and some equivalences of this property have been investigated. In the process of investigating semilattices, the author found a class of semigroups called coverable semigroups, and the interesting fact about it is that a necessary and sufficient condition for a compact semilattice to have small semilattices is to be coverable. Also by virtue of the concept of coverable semigroups, one can show that the usual interval is costable instead of the more intricate method of proving it by producing an arc.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0310122-5
Keywords: Small semilattices, codimension, costable semigroups, totally disconnected semigroups, min intervals, usual intervals
Article copyright: © Copyright 1973 American Mathematical Society