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A One-Parameter Subsemigroup which meets many Regular -Classes

Published online by Cambridge University Press:  20 November 2018

E. D. Tymchatyn
E. D. Tymchatyn*
Affiliation:
University of Oregon, Eugene, Oregon; University of Saskatchewan, Saskatoon, Saskatchewan
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We give an example which answers affirmatively the following problem posed by Hofmann and Mostert (1, p. 200):

P. 10. Let S be a compact semigroup with identity 1, zero 0, and totally ordered -class space . Suppose that there is a one-parameter semigroup containing 0 and 1. Can S have any regular -classes aside from D(0) and D(1)?

I am indebted to Professor K. H. Hofmann and Professor P. S. Mostert for their many helpful suggestions.

1. We first give a method of embedding a given semigroup S in a semigroup R so that in the commutative diagram

the bottom map is an isomorphism of partially ordered spaces and some non-regular -class of S is embedded into a regular -class of R.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 735 - 739
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Hofmann, K. H. and Mostert, P. S., Elements of compact semigroups (Charles E. Merrill Books, Columbus, Ohio, 1966).Google Scholar