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Embedding any countable semigroup in a 2-generated bisimple monoid

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
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G. B. Preston [10] proved that any semigroup can be embedded in a bisimple monoid. If S is a countable semigroup, his constructive proof yields a bisimple monoid which is also countable, but not necessarily finitely generated. The main result of this paper is that any countable semigroup can be embedded in a 2-generated bisimple monoid.

J. M. Howie [6] proved that any semigroup can be embedded in an idempotentgenerated semigroup. F. Pastijn [9] showed that any semigroup can be embedded in a bisimple idempotent-generated semigroup, and that any countable semigroup can be embedded in a semigroup which is generated by 3 idempotents. Easy proofs of these results using Rees matrix semigroups over a semigroup were given by the author [3]. In this paper, as a corollary to our main result, we deduce that any countable semigroup can be embedded in a bisimple semigroup which is generated by 3 idempotents.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 25 , Issue 2 , July 1984 , pp. 153 - 161
Copyright
Copyright © Glasgow Mathematical Journal Trust 1984

References

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