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Embedding any countable semigroup without idempotents in a 2-generated simple semigroup without idempotents

Published online by Cambridge University Press:  18 May 2009

Karl Byleen
Karl Byleen
Affiliation:
Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, Wisconsin 53233, USA
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Although the classes of regular simple semigroups and simple semigroups without idempotents are evidently at opposite ends of the spectrum of simple semigroups, their theories involve some interesting connections. Jones [5] has obtained analogues of the bicyclic semigroup for simple semigroups without idempotents. Megyesi and Pollák [7] have classified all combinatorial simple principal ideal semigroups on two generators, showing that all are homomorphic images of one such semigroup Po which has no idempotents.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 30 , Issue 2 , May 1988 , pp. 121 - 128
Copyright
Copyright © Glasgow Mathematical Journal Trust 1988

References

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